Digital ece

Fundamentals of
Digital Electronics
by Professor Barry Paton
Dalhousie University

March 1998 Edition
Part Number 321948A-01

Fundamentals of Digital Electronics

Copyright
Copyright © 1998 by National Instruments Corporation, 6504 Bridge Point Parkway, Austin, Texas 78730-5039.
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Contents

Introduction

Lab 1
Gates
The AND Gate...............................................................................................1-1
The OR and XOR Gates ................................................................................1-2
Negation.........................................................................................................1-2
The NAND, NOR, and NXOR Gates............................................................1-2
Building Gates from Other Gates ..................................................................1-3
Gates with More than Two Inputs .................................................................1-4
Masking .........................................................................................................1-5
Application: Data Selector.............................................................................1-6
Name that Gate ..............................................................................................1-6
Lab 1 Library VIs ..........................................................................................1-6

Lab 2
Encoders and Decoders
The Die ..........................................................................................................2-2
Modulo 6 Counter..........................................................................................2-3
Encode ...........................................................................................................2-4
Virtual Dice ...................................................................................................2-5
Lab 2 Library VIs ..........................................................................................2-6

Lab 3
Binary Addition
Adder Expansion (Half Adder, Full Adders).................................................3-3
Binary Coded Decimal (BCD).......................................................................3-5
LabVIEW Challenge .....................................................................................3-6
Lab 3 Library VIs ..........................................................................................3-6

© National Instruments Corporation iii Fundamentals of Digital Electronics

Contents

Lab 4
Memory: The D-Latch
Shift Registers................................................................................................4-2
LabVIEW Challenge: The Bucket Brigade ...................................................4-4
Ring Counters ................................................................................................4-4
Lab 4 Library VIs ..........................................................................................4-5

Lab 5
Pseudo-Random Number Generators
A 6-Bit Pseudo-Random Number Generator.................................................5-1
An 8-Bit Pseudo-Random Sequencer ............................................................5-2
8-Bit Pseudo-Random Number Generator.....................................................5-5
Encryption of Digital Data.............................................................................5-6
Lab 5 Library VIs ..........................................................................................5-7

Lab 6
JK Master-Slave Flip-Flop
Binary Counters (1-Bit, 2-Bit, and 4-Bit) ......................................................6-3
8-Bit Binary Counter (with and without Reset).............................................6-5
Summary ........................................................................................................6-5
Lab 6 Library VIs ..........................................................................................6-6

Lab 7
Digital-to-Analog Converter
What is a DAC? .............................................................................................7-1
ALU Simulator ..............................................................................................7-3
Simulating a Real DAC Chip.........................................................................7-4
Waveform Generators....................................................................................7-5
Special DACs.................................................................................................7-6
Lissajous Figures ...........................................................................................7-7
Lab 7 Library VIs ..........................................................................................7-8
Lab 8
Analog-to-Digital Converters, Part I
Purpose of the Analog-to-Digital Converter..................................................8-1
The Ramp ADC .............................................................................................8-2
Tracking ADC................................................................................................8-4
Lab 8 Library VIs ..........................................................................................8-6

Lab 9
Analog-to-Digital Converters, Part II
SAR Simulation .............................................................................................9-3
Summary ........................................................................................................9-4
Lab 9 Library VIs ..........................................................................................9-4

Fundamentals of Digital Electronics iv © National Instruments Corporation

Contents

Lab 10
Seven-Segment Digital Displays
Seven-Segment Display .................................................................................10-1
Lab 10 Library VIs ........................................................................................10-5

Lab 11
Serial Communications
Serial Transmitter ..........................................................................................11-2
Voltage to Serial Transmitter.........................................................................11-4
Lab 11 Library VIs ........................................................................................11-5

Lab 12
Central Processing Unit
Operation of the Arithmetic and Logic Unit..................................................12-2
The Accumulator ...........................................................................................12-3
Addition .........................................................................................................12-4
Binary Counter...............................................................................................12-5
Lab 12 Library VIs ........................................................................................12-6

© National Instruments Corporation v Fundamentals of Digital Electronics

Introduction

Digital electronics is one of the fundamental courses found in all electrical
engineering and most science programs. The great variety of LabVIEW
Boolean and numeric controls/indicators, together with the wealth of
programming structures and functions, make LabVIEW an excellent tool to
visualize and demonstrate many of the fundamental concepts of digital
electronics. The inherent modularity of LabVIEW is exploited in the same
way that complex digital integrated circuits are built from circuits of less
complexity, which in turn are built from fundamental gates. This manual
is designed as a teaching resource to be used in the classroom as
demonstrations, in tutorial sessions as collaborative studies, or in the
laboratory as interactive exercises.
The order of the labs follows most electronic textbooks. The first six labs
cover the fundamental circuits of gates, encoders, binary addition,
D-latches, ring counters, and JK flip-flops. Many of the VIs are suitable for
both classroom demonstration and laboratory exploration.
The second set of six labs cover advanced topics such as DACs, ADCs,
seven-segment displays, serial communication, and the CPU. These are best
done in the context of a digital electronics lab, comparing the LabVIEW
simulations with real integrated circuits. In each case, you can enhance
simulations presented in the text by using a National Instruments DAQ
board to interact with the real world through LabVIEW digital I/O, analog
out, analog in, and serial VIs.
Labs 2, 5, and 12 are application oriented and are designed to demonstrate
encoding schemes, digital encryption, and the operation of a CPU. These
labs could be presented as challenging problems in a tutorial setting or in a
workshop environment.
The labs can also be grouped to demonstrate special relationships of
advanced devices on certain basic gates. For example, the CPU operation is
dependent on the concept of registers and two input operations.
This manual includes a complete set of LabVIEW VIs. The text is also
included on the CD so that you can customize the material.

© National Instruments Corporation I-1 Fundamentals of Digital Electronics

Lab 1
Gates

Gates are the fundamental building blocks of digital logic circuitry. These
devices function by “opening” or “closing” to admit or reject the passage of
a logical signal. From only a handful of basic gate types (AND, OR, XOR,
and NOT), a vast array of gating functions can be created.

The AND Gate
A basic AND gate consists of two inputs and an output. If the two inputs
are A and B, the output (often called Q) is “on” only if both A and B are
also “on.”

In digital electronics, the on state is often represented by a 1 and the off state
by a 0. The relationship between the input signals and the output signals is
often summarized in a truth table, which is a tabulation of all possible inputs
and the resulting outputs. For the AND gate, there are four possible
combinations of input states: A=0, B=0; A=0, B=1; A=1, B=0; and A=1, B=1.
In the following truth table, these are listed in the left and middle columns.
The AND gate output is listed in the right column.

Table 1-1. Truth Table for AND Gate

A B Q=A AND B
0 0 0
0 1 0
1 0 0
1 1 1

© National Instruments Corporation 1-1 Fundamentals of Digital Electronics

Lab 1 Gates

In LabVIEW, you can specify a digital logic input by toggling a Boolean
switch; a Boolean LED indicator can indicate an output. Because the AND
gate is provided as a basic built-in LabVIEW function, you can easily wire
two switches to the gate inputs and an indicator LED to the output to
produce a simple VI that demonstrates the AND gate.

Figure 1-1. LabVIEW AND Function Wired to I/O Terminal Boxes

Run AND gate.vi from the Chap 1.llb VI library. Push the two input buttons
and note how the output indicator changes. Verify the above truth table.

The OR and XOR Gates
The OR gate is also a two-input, single-output gate. Unlike the AND gate,
the output is 1 when one input, or the other, or both are 1. The OR gate
output is 0 only when both inputs are 0.

A A
OR Q XOR Q
B B

Figure 1-2. Digital Symbols for the OR and XOR Gates

A related gate is the XOR, or eXclusive OR gate, in which the output is 1
when one, and only one, of the inputs is 1. In other words, the XOR output
is 1 if the inputs are different.

Negation

A A

Figure 1-3. The NOT Gate

An even simpler gate is the NOT gate. It has only one input and one output.
The output is always the opposite (or negation) of the input.

The NAND, NOR, and NXOR Gates
Negation is quite useful. In addition to the three two-input gates already
discussed (AND, OR, and XOR), three more are commonly available. These
are identical to AND, OR, and XOR, except that the gate output has been

Fundamentals of Digital Electronics 1-2 © National Instruments Corporation

Lab 1 Gates

negated. These gates are called the NAND (“not AND”), NOR (“not OR”),
and NXOR (“not exclusive OR”) gates. Their symbols are just the symbols
of the unnegated gate with a small circle drawn at the output:

A
Q
B

A
Q
B

A
Q
B

Figure 1-4. Negated AND, OR, and XOR Gates

Run Truth table.vi. Choose a gate and try all combinations of A and B to
complete the following truth tables.

Table 1-2. Truth Tables for the Digital Logic Basic Gates

A B AND OR XOR NAND NOR NXOR
0 0 0
0 1 0
1 0 0
1 1 1

Building Gates from Other Gates
Given a handful of NAND gates, you can reproduce all other basic logic
gates. For example, you can form the NOT gate by connecting both NAND
input terminals to the same input:

Figure 1-5. NOT Gate Built from a NAND Gate

Similarly, you can easily build an AND gate from two NAND gates:

Figure 1-6. AND Gate from Two NAND Gates


Lab 1 Gates

An OR requires three NAND gates:

Figure 1-7. OR Gate from Three NAND Gates

Construct a VI that demonstrates that an XOR gate can be constructed from
four NAND gates. For reference, see XOR from NAND.vi in the Lab 1 VI
library.

Gates with More than Two Inputs
Although LabVIEW includes all the basic two-input gates, you may require
more inputs. For example, the AND truth table above can be generalized to
three inputs:

Table 1-3. Truth Table for a Three-Point Input AND Gate

A B C A AND B AND C
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 1

From a pair of two-input AND gates, you can easily build a VI that
implements the three-input AND:

Figure 1-8. LabVIEW Program for a Three-Input AND Gate

Open the VI called 3 AND.vi and notice the socket and icon, making this VI
a full-fledged subVI.


Lab 1 Gates

Masking
As a simple application of how these basic logic gates can be combined,
consider the concept of masking. To illustrate this concept, below is the
AND truth table with relabeled column headings.

Table 1-4. Truth Table for AND Gate with One Input as a Mask

A Mask A AND B Effect
0 0 0
A is blocked Gate is “closed”
1 0 0
0 1 0
A is unchanged Gate is “open”
1 1 1

The truth table makes the point that the AND gate can be used as an
electronic switch.

This point is easily demonstrated in LabVIEW:

Figure 1-9. AND Gate Used as an Electronic Switch

Load and run E-switch.vi to observe the electronic switch in action. You can
view the truth tables of other gates from a masking point of view as well. In
the following table, reset means “forced to 0” while set means “forced to 1”:

Table 1-5. Truth Table for AND, OR and XOR Gates with One Input as a Mask

A Mask AND OR XOR
0 0
A is reset A is unchanged A is unchanged
1 0
0 1
A is unchanged A is set A is inverted
1 1

In summary, there are three useful functions here. To set a state, use OR with
a mask of 1. To reset a state, use AND with a mask of 0. To invert a state,
use XOR with a mask of 1.


Lab 1 Gates

Application: Data Selector
Another simple application of basic gates is the data selector, in which a
single digital input selects one of two digital streams:

Figure 1-10. A Digital Data Selector Built with Basic Gates

LabVIEW includes a built-in function, called Select, to emulate this
operation. Thus, you could rewire the above as:

Figure 1-11. LabVIEW’s Version of a Digital Data Selector

Name that Gate
The gates in this section form the foundation of much of digital electronics.
A complete familiarity with the truth tables is extremely useful. As a review,
test your skills with the Name that gate VI.

Lab 1 Library VIs (Listed in the Order Presented)
• AND gate.vi (two-input AND operation)
• Truth table.vi (for AND, OR, XOR, NAND, NOR, and NXOR)
• XOR from NAND.vi
• 3 AND.vi (three-input AND operation)
• Masking.vi (demonstration)
• E-switch.vi (electronic switch)
• Data select.vi (data selector using basic logic gates)
• Data select2.vi (data selector using the LabVIEW Select function)
• Oscillator.vi (subVI used in Data select.vi)
• Name that gate.vi (test your knowledge)


Lab 2
Encoders and Decoders

An encoder converts an input device state into a binary representation of
ones or zeros. Consider a rotary switch with 10 positions used to input the
numbers 0 through 9. Each switch position is to be encoded by a unique
binary sequence. For example, switch position 7 might be encoded as 0111.
A decoder performs the opposite conversion, from binary codes into output
codes.

Consider the case of a single die. On each of its six sides, one of the
following patterns appears, representing the numbers 1-6.

Figure 2-1. The Six Sides of a Die

These patterns are traditional. They can be thought of as seven lights
arranged in an “H” pattern:

Figure 2-2. Dot Arrangement Used in Dice Codes

By turning on the appropriate lights, you can create any of the six patterns
on the face of a die.


Lab 2 Encoders and Decoders

On closer inspection, there are only four unique patterns from which the
pattern for any face can be formed. Call these base patterns A, B, C, and D:

A B C D
Figure 2-3. Four Base Patterns Used in Dice Codes

If you write down the truth table, for the presence or absence of these base
patterns as a function of die face, the meaning of these base states becomes
clear.

Table 2-1. Base States Used for Each Die Number

Die Face A B C D
1 √
2 √
3 √ √
4 √ √
5 √ √ √
6 √ √ √

The base pattern A is used by all odd numbers (1, 3, and 5). Pattern B is in
the representation of all of the numbers except 1. Base pattern C is found in
the numbers 4, 5, and 6. Pattern D is used only when representing 6.

The Die
To build a virtual die, place seven LED indicators in the “H” pattern on the
front panel, together with four switches. On the diagram page, the LED
terminals are wired to display the four unique patterns A, B, C, and D. The
four switches on the front panel can now simulate turning on and off the base
patterns.

Figure 2-4. LabVIEW Front Panel for Virtual Die Display



Figure 2-5. LabVIEW Block Diagram to Implement Virtual Die Display

Load the VI Display.vi and observe the operation of the virtual die.

Modulo 6 Counter
A modulo 6 counter is any counter with six unique states that repeat in
sequence. You can build a simple modulo 6 counter using a three-element
shift register with the last element output inverted and feedback into the first
element input. (Such a counter is often called a switched tail ring counter.)

Open a new LabVIEW VI. Place three LED indicators on the front panel.
These will show the output state of the shift register elements called Q1, Q2,
and Q3. On the block diagram, use a shift register with three elements, each
wired to one LED indicator. You can use a Wait function to slow down the
action for demonstration. Note that the While Loop control is left unwired.
Each time this VI is called, the next value is returned. On the front panel,
select the three outputs as connections in the icon editor and save this
program as a subVI called Rotate.vi.

Figure 2-6. Rotate.vi Front Panel and Block Diagram



Below is the truth table for the modulo 6 counter. Run the program seven
times to observe the action.

Table 2-2. Truth Table for Modulo 6 Counter

Cycle Q1 Q2 Q3
1 0 0 0
2 1 0 0
3 1 1 0
4 1 1 1
5 0 1 1
6 0 0 1
7 0 0 0 same as cycle 1

The output repeats after six counts, hence the name modulo 6 counter.

Encoder
There is no a priori reason to decide which output corresponds to which
count. However, a little foresight makes the choices easier:

Table 2-3. Digital Die Encoding Scheme

# Q1 Q2 Q3 Q1′ Q2′ Q3′
6 0 0 0 1 1 1
4 1 0 0 0 1 1
2 1 1 0 0 0 1
1 1 1 1 0 0 0
3 0 1 1 1 0 0
5 0 0 1 1 1 0

For example, each output has three (1) states and three (0) states. One of
these outputs, for example Q3, could signify odd states 1, 3, and 5. Another
output state, for example Q2′, can then signify the family 4, 5, 6. These two
lines then decode two of the base patterns for “free.” The two remaining
base patterns are decoded with a particular pattern of the three counter
lines. To this end, a three-input AND gate built in the last lab together with
an inverter can be used. Not 1 (Base Pattern B) is decoded with the
combination Q1 & Q2 & Q3, and the final base state “6” is decoded with
Q1′ & Q2′ & Q3′.



Figure 2-7. Encode.vi Front Panel and Block Diagram

The encoder is built by placing three Boolean indicators on the front panel
together with four LED indicators. The encoder is wired by translating the
words of the above paragraph into a circuit.

Virtual Dice

(modulo 6)

Counter Encoder

stop

Figure 2-8. Function Schematic for Digital Dice

To roll the virtual die, a high-speed counter will cycle through the six states.
These states are encoded on three output lines. In practice, the counter
cycles until a stop command is issued to the counter. Whatever state the
counter has on its output will be the roll value. A clock with a speed greater
than 1 kHz ensures the randomness of the roll.

An encoder VI converts the three counter lines into the four control lines for
the base patterns. These in turn set the dots on the virtual die to the correct
output code.

It is now a simple case of assembling all the components—counter, encoder
and display—into a VI called Dice.vi. Just as you would build electronic
circuits by assembling gates, latches, switches, and displays, LabVIEW
simulates this process by building complex functions from simpler ones.



Figure 2-9. Dice.vi Block Diagram. Note the Similarity with the Function Schematic Above

Now, flip the front panel switch and let the good times roll!

• Display.vi (LED displays for virtual die)
• Rotate.vi (modulo 6 counter)
• Encoder.vi (converts counter codes to display codes)
• 3 AND.vi (subVI used in Encoder.vi)
• Dice.vi (let the good times roll)


Lab 3
Binary Addition

Before proceeding with this lab, it is helpful to review some details of binary
addition. Just as in decimal addition, adding 0 to any value leaves
that number unchanged: 0 + 0 = 0, while 1 + 0 = 1. However, when you add
1 + 1 in binary addition, the result is not “2” (a symbol which does not exist
in the binary number system), but “10”; a “1” in the “twos place” and a zero
in the “ones place.” If you write this addition vertically, you would recite,
“One and one are two; write down the zero, carry the one”:
1
+1
10
Figure 3-1. Single-Bit Addition

Below is the truth table for single-bit addition. There are two input columns,
one for each addend, A1 and A2, and two output columns, one for the
ones-place sum and one for the carried bit:

Table 3-1. Truth Table for Addition

A1 + A2 = Sum with Carry
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1


Lab 3 Binary Addition

Which of the fundamental gates can you use to implement the output
columns? Note that A1 XOR A2 reproduces the Sum output, and A1 AND
A2 the Carry output, so a LabVIEW implementation of this 1-bit addition
truth table is

Figure 3-2. Half Adder Built from XOR and AND Gates

This digital building block is called a “half adder.” The term “half adder”
refers to the fact that while this configuration can generate a signal to
indicate a carry to the next highest order bit, it cannot accept a carry from a
lower-order adder.

A “full adder” has three inputs. In addition to the two addends, there is also
a “carry in” input, which adds the bit carried from the previous column, as
in the middle column in the following example:
101
+101
1010
Figure 3-3. Three-Bit Binary Addition

The truth table for a single-bit full adder therefore has three inputs, and thus
eight possible states:

Table 3-2. Truth Table for Addition with a Carry In

Carry In A1 A2 Sum Carry Out
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1



Note that all three inputs are essentially equivalent; the full adder simply
adds the three inputs. One way to build a 1-bit full adder is by combining
two half adders:

Figure 3-4. Full Adder Using Two Half Adder SubVIs

Note the simplicity achieved in the wiring diagram by using the half adders.

Adder Expansion
You can construct a device that adds multibit binary numbers by combining
1-bit adders. Each single-bit adder performs the addition in one “column” of
a sum such as
1011
+0010
1101
Figure 3-5. 4-Bit Binary Addition (11+2=13)

For example, a 4-bit adder could be constructed in LabVIEW as:

Figure 3-6. LabVIEW Block Diagram for 4-Bit Binary Addition

Note that this VI uses four 1-bit full adders. If you plan to add only 4-bit
numbers with this circuit, the lowest-order adder could be a half adder. The



use of all full adders allows the 4-bit adder to have a carry-in input, as well
as the two 4-bit addend inputs. Load Four-bit Adder1.vi and observe the
addition of two 4-bit numbers. It uses two subVIs, Full Adder.vi, shown in
Figure 3-4, and Half Adder.vi, shown in Figure 3-2.

As you can see, the wiring above is somewhat complicated and would
become even more complex if you extended the adder to more bits. By using
a LabVIEW For Loop with a shift register, you can simplify the wiring
significantly:

Figure 3-7. 4-Bit Binary Addition Using LabVIEW Arrays (Four-Bit Adder2.vi)

Note how the four independent bits are formed into 4-bit arrays before
passing into the interior of the For Loop, which iterates four times, each time
adding a pair of bits, starting at the least significant bit. On the first iteration,
the carry input to the 1-bit full adder is from the panel carry input; on
subsequent iterations, it is the carry from the previous iteration. Run both
versions of the VI and confirm that their behaviors are identical.

Figure 3-8. 4-Bit Adder Using Array Inputs and Outputs



There is also a third version of the above VI, named simply Four-bit
Adder3.vi, which is identical to Figure 3-7 above except that the inputs and
outputs are displayed as Boolean arrays. Note that in Boolean arrays, the
LSB is on the left and the MSB is on the right. This version has been
configured as a subVI, and you can combine two of these to create an 8-bit
adder. Note that each 8-bit (one-byte) addend is separated into two 4-bit
“nibbles,” and then the two “least significant nibbles” are sent to one 4-bit
adder, while the two “most significant nibbles” go to a second 4-bit adder.

Figure 3-9. 8-Bit Adder Using Two 4-Bit Adders

Binary Coded Decimal (BCD)
Not all digital arithmetic is performed by a direct conversion to the base-2
representation. Binary coded decimal, or BCD, representation is also used.
In BCD, each decimal digit is separately encoded in four bits as follows:

Table 3-3. BCD Representation for the Numbers 0 to 9

Decimal Digit BCD Representation Decimal Digit BCD Representation
0 0000 5 0101
1 0001 6 0110
2 0010 7 0111
3 0011 8 1000
4 0100 9 1001

BCD can be considered to be a subset of full binary notation, in which only
the states 0000 to 1001 (0 to 9) are used. For example,

42 10 = 0100 0010 BCD



Note that this is distinct from the binary representation, which in this case
would be

42 10 = 00101010 2

Clearly, BCD is wasteful of bits, because there are a number of 4-bit patterns
that are not used to encode a decimal digit. The waste becomes more
pronounced for larger integers. Two bytes (16 bits) is enough to encode
unsigned decimal integers in the range 0-65535 if the binary representation
is used, but the same two bytes will span only the range 0-9999 when using
BCD. The advantage of BCD is that it maps cleanly to decimal output
displays.

LabVIEW Challenge
Create a BCD encoder that takes as its input a digit in the range 0-9 and
outputs the 4-bit BCD representation. Build a BCD decoder that reverses the
behavior of the above encoder. Build a one-digit BCD adder.

• Half Adder.vi (single-bit addition)
• Full Adder.vi (single-bit addition with carry in)
• Four-bit Adder1.vi (adds two 4-bit numbers with carry in)
• Four-bit Adder2.vi (simplified version)
• Four-bit Adder3.vi (uses Boolean arrays for inputs and outputs)
• Eight-bit Adder.vi (uses two 4-bit adders)


Lab 4
Memory: The D-Latch

In the first three labs in this series, all your work has been with
combinational circuits in which the input states completely determine the
output states. In the circuits thus far, there is no dependence on past history
or how you arrived at the current state. This means that “remembering”
cannot be built into the circuits. Most digital operations are sequential, in
that event B must occur after event A. Furthermore, in a digital computer,
events are not only sequential but also synchronous with some external
clock. Clocked logic devices are devices whose output changes only when
a clock signal is asserted. In the next few labs, you will see how the addition
of clocked logic devices brings memory into digital circuits, making it
possible to construct many interesting digital circuits.

One simple memory circuit is called the data latch, or D-latch. This is a
device which, when “told” to do so via the clock input, notes the state of its
input and holds that state at its output. The output state remains unchanged
even if the input state changes, until another update request is received.
Traditionally, the input of the D-latch is designated by D and the latched
output by Q. The update command is provided by asserting the clock input
in the form of a transition (from HI to LO) or (from LO to HI), so-called
edge-triggered devices or level triggered devices, where the output follows
the input whenever the clock is HI.


Lab 4 Memory: The D-Latch

PreSet
D Q Q Set Clr Q Q
0 0 1 0 0 disallowed
D Q
1 1 0 0 1 1 0
1 0 0 1
Clock Q clocked logic 1 1 clocked

Clr

Figure 4-1. D-Latch Symbol and Truth Tables

Data present on the input D is passed to the outputs Q and Q when the clock
is asserted. The truth table for an edge-triggered D-latch is shown to the
right of the schematic symbol. Some D-latches also have Preset and Clear
inputs that allow the output to be set HI or LO independent of the clock
signal. In normal operation, these two inputs are pulled high so as not to
interfere with the clocked logic. However, the outputs Q and Q can be
initialized to a known state, using the Preset and Clear inputs when the
clocked logic is not active.

Figure 4-2. LabVIEW Simulation of a D-Latch

In LabVIEW, you can simulate the D-latch with a shift register added to a
While Loop. The up-arrow block is the D input, and the down-arrow block
is the output Q. The complement is formed with an inverter tied to the Q
output. The clock input is analogous with the loop index [i]. You can use a
Boolean constant outside the loop to preset or clear the output. D Latch.vi,
shown above, uses an unwired conditional terminal to ensure that the
D-latch executes only once when it is called.

Shift Registers
In digital electronics, a shift register is a cascade of 1-bit memories in which
each bit is updated on a clock transition by copying the state of its neighbor.



Q1 Q2 Q3 Q4

HI or LO D Q D Q D Q D Q

Q Q Q Q

Clock

Figure 4-3. 4-Bit Shift Register

The bits at the ends have only one neighbor. The input bit D is “fed” from
an external source (HI or LO), and the output Q4 spills off the other end of
the shift register. Here is an example of a 4-bit shift register whose initial
output state is [0000] and input is [1]:

Clock Cycle Q1 Q2 Q3 Q4
n 0 0 0 0
n+1 1 0 0 0
n+2 1 1 0 0
n+3 1 1 1 0
n+4 1 1 1 1

To “cascade” D-latches as above in LabVIEW, additional elements are
added to the D-latch shift register. For example, here is the 4-bit register.
Shift.vi executes the above sequence.

Figure 4-4. Block Diagram for an 8-Bit Shift Register

It is a simple matter to add additional elements to simulate larger width shift
registers. The following VI, Bucket.vi, simulates a “bucket brigade” where
a single bit is introduced on the input D and propagates down the line, where
it spills out and is lost after passing Q8.



Figure 4-5. Front Panel of an 8-Bit Shift Register Simulation

LabVIEW Challenge
Design a VI in which after the “bucket” passes the last bit, a new bucket is
added at the input D, and the process continues forever.

Ring Counters
If the output of a shift register is “fed” back into the input, after n clock
cycles, the parallel output eventually will repeat and the shift register now
becomes a counter. The name ring counter comes from looping the last
output bit back into the input. A simple 4-bit ring counter takes the last
output, Q4, and loops it back directly to the input of the shift register, D.

Q1 Q2 Q3 Q4

D Q D Q D Q D Q

Q Q Q Q

Clock

Figure 4-6. 4-Bit Ring Counter Using Integrated Circuit Chips

In the above case, the outputs have been preset to [0110]. Load and run
Rotate.vi. Observe how the outputs cycle from [0110] to [0011] to [1001]
to [1100] and back to [0110]. It takes four clock cycles, hence this counter
is a modulo 4 ring counter. In a special case where these four outputs are
passed to the current drivers of a stepping motor, each change in output
pattern results in the stepping motor advancing one step. A stepping motor
with a 400-step resolution would then rotate 0.9 degrees each time the
counter is called. A slight variation of the ring counter is the switched tail
ring counter. In this case, the complement output Q of the last stage is fed
back into the input. Modify Rotate.vi to make this change and save it as
Switch Tail Ring Counter.vi.



What is the modulus of the switch tail ring counter?

Ring counters are often used in situations where events must be repeated at
a uniform rate. Load and observe Billboard.vi, shown below, which
simulates a light chaser.

You can use the slide control to set the speed of the changing lights, and the
16 Boolean constants on the block diagram set the chase pattern.

• D Latch.vi (LabVIEW simulation of a data latch)
• Shift.vi (4-bit shift register)
• Bucket.vi (8-bit shift register simulation)
• Rotate.vi (4-bit ring counter)
• Billboard.vi (16-bit ring counter used as a light chaser)



Notes


Lab 5
Pseudo-Random Number
Generators

In the last lab, simple ring counters were introduced as a means of building
modulo-n counters. In this lab, feedback from a combination of advanced
stages is combined and routed back into the input gate. If the correct
combination is chosen, the output is of maximal length (that is, the modulus
of the counter is 2N-1). For an 8-bit counter, N = 8 and (2N-1) = 255. These
circuits, often called pseudo-random number generators (PRNG), have
some interesting features. The sequences formed appear to be random over
the short range, but in fact the sequence repeats after (2N-1) cycles.
Furthermore, each pattern occurs only once during each sequence of (2N-1)
numbers.

Pseudo-random sequence and number generators have wide applications in
computer security, cryptography, audio systems testing, bit error testing, and
secure communications.

A 6-Bit Pseudo-Random Number Generator
In the following circuit, the outputs of the fifth and sixth D-latches have
been exclusive NORed together to become the input to the shift register. It
is assumed that initially, all outputs are zero.

D Q D Q D Q D Q D Q D Q
1 2 3 4 5 6
C C C C C C

Clock

Figure 5-1. 6-Bit PRNG Built from Six D-Latches and an XOR Gate


Lab 5 Pseudo-Random Number Generators

When Q5 and Q6 are 0, the output of the NXOR (see Lab 1) is 1. This HI
value is loaded into the shift register at the input D1. On command from the
clock, all bits shift to the right. The initial value of (000000) goes to
(100000). It is easy to work through a few cycles to see the outputs Q1...Q6
follow the sequence:
(000000)
(100000)
(110000)
(111000)
----------

After 63 cycles, the sequence returns to the initial state (000000).

It is easy to simulate this circuit with a LabVIEW VI.

Figure 5-2. LabVIEW VI to Simulate a 6-Bit PRNG

A six-element shift register is placed on a While Loop. An exclusive OR
gate and inverter are used for the NXOR gate whose inputs have been wired
to Q5 and Q6. The loop index keeps track of the cycle count, and a delay of
500 ms allows the reader to observe the PRNG patterns. When running this
VI, 6PRNG.vi, observe that cycles 0 and 63 are the same (that is, all bits are
zero).

An 8-Bit Pseudo-Random Sequencer
An 8-bit PRNG uses the outputs Q4, Q5, Q6, and Q8 NXORed together to
form the maximal length (2N-1) count sequence of 255.



Figure 5-3. LabVIEW Simulation of an 8-Bit PRNG

As in the previous example, the parallel output can be observed on eight
LED indicators. In addition, a pseudo-random sequence of ones and zeros is
produced at Serial Out.

Many digital circuits need to be tested with all combinations of ones and
zeros. A “random” Boolean sequence of ones and zeros at [Serial Out]
provides this feature. In this configuration, the circuit is called a
pseudo-random bit sequencer, PRBS. On the front panel of the above VI,
PRBS0.vi, you can view the Boolean sequence [Serial Out] on an LED
indicator.

Figure 5-4. Front Panel of the 8-Bit PRBS



A better way to view the bit sequence is as a bit trace. The Boolean bits are
converted into a numeric value of either 1 or 0 and then plotted on a
LabVIEW chart. Here, the first 50 bits from PRBS.vi are displayed as a
logic trace.

Figure 5-5. Serial Output from the Pseudo-Random Bit Sequencer

Communication lasers are tested using PRBS waveforms. Sometimes a laser
may lock up from a particular sequence of ones and zeros, or a bit level may
be outside specifications. The laser output is detected by a photodiode,
converted into a digital signal, and passed to one side of a digital
comparator. At the same time, the PRBS driving sequence is passed to the
other input of the comparator. Any errors in transmission or lockup can be
flagged.

It is now easy to verify that the bit sequence repeats exactly after 255 cycles.
In PRBS2.vi, two charts display the sequence. By resetting the scale of the
second chart from 255 to 305, you can observe the repetitive nature of
the PRBS.

Figure 5-6. Comparison of the First 50 Binary Bits from a PRBS with Bits 255-305



8-Bit Pseudo-Random Number Generator
The addition of an analog-to-digital converter allows the parallel outputs of
the pseudo-random number sequence to be converted into a numeric
number. In a binary conversion, the parallel bits (Q1...Q8) are weighted as
(1, 2, 4, 8, 16, 32, 64, and 128). In the following VI, the numeric values are
displayed on a three-digit display and chart on the front panel.

Figure 5-7. Numeric Output from an 8-Bit PRNG

Running PRNG.vi allows you to observe the PRNG sequence of numbers.
All the numbers from 0 to 254 will be found in the PRNG sequence, and on
closer inspection, each number will appear only once in the sequence. Does
the sequence appear random?

The following block diagram is the LabVIEW simulation of an 8-bit PRNG.
Note how the DAC displays the numerical values of the Boolean parallel
outputs.

Figure 5-8. LabVIEW Program for the 8-Bit PRNG with Chart Output



The chart format conveniently displays the analog sequence. Over the short
range (10-30) numbers, the output appears random and in fact is random
from a mathematical perspective. As an analog output, it appears as white
noise. The value of PRNG in audio testing is that the noise repeats after 2N-1
cycles. Amplifiers like digital gates may have short-term memory, but not
long-term memory. The PRNG analog output is applied to the analog circuit
under test. Its output is compared with the expected levels from the PRNG
sequence. Any deviation (errors) can reveal problems with the circuit under
test.

Encryption of Digital Data
Most data communication takes the form of ASCII characters. The addition
of a parity bit to 7-bit ASCII codes yield an 8-bit digital number. Banking
machines, electronic door locks, and computer passwords all use ASCII
data and some form of encryption to preserve security.

The 8-bit PRNG is a useful circuit for encryption of ASCII data. All cases
thus far have used the LabVIEW default initialization of the shift register to
start the PRNG sequence. In fact, the sequence can begin at any initial value
except the disallowed state (11111111). Suppose the initial value was
(01111010), or 122 in numeric, or $7A in HEX, or the character “z” in
ASCII. The PRNG sequence is just offset by this value, but the sequence
repeats itself in the usual way, repeating after 255 cycles. Below is a
Boolean array representation of 8-bit PRNG values starting at some
index (7) and the next six values. Note that after 255 cycles plus this index
(7 + 255 = 262), the sequences are identical, hence predictable.

Figure 5-9. Boolean Array Representation of the 8-Bit Binary Pattern of the First Eight
Numbers of an 8-Bit PRNG with the Patterns for Loops 262 to 268

Suppose a PIN or password is used to form a unique numeric code number,
N. The PRNG is initialized by an ASCII character, and the PRNG converts
this input character into an encrypted character by clocking the PRNG ahead
N cycles. When completed, the parallel outputs contain the encrypted
character. In the above example, if the PIN number was 257, the character
“z” would be encrypted as “X.” For each character in a message, a new



character is formed. The receiver knows the encryption algorithm, and with
the PIN, the original message can be deciphered.

• 6PRNG.vi (6-bit PRNG)
• PRBS0.vi (8-bit pseudo-random bit sequencer)
• PRBS.vi (8-bit PRBS with serial output on chart)
• PRNG.vi (8-bit PRNG with chart output)
• PRNG7.vi (8-bit PRNG with array outputs)
• DAC8.vi (8-bit DAC subVI)



Notes


Lab 6
JK Master-Slave Flip-Flop

One of the most important clocked logic devices is the master-slave JK
flip-flop. Unlike the D-latch, which has memory only until another clock
pulse comes along, the JK flip-flop has true memory. When the J and K
inputs are low, the state of the outputs Q and Q are unchanged on clocking.
Thus, information can be placed onto the output bit and held until requested
at a future time. The output Q can be clocked low or high by setting the (J,K)
inputs to (0,1) or (1,0), respectively. In fact, placing an inverter between J
and K inputs results in a D-latch circuit. The schematic diagram for the JK
flip-flop and its truth table is shown below. Note that the JK flip-flop can
also be Set or Reset with direct logic inputs.

Set
clock J K Q Q Set Clr Q Q
0 0 no change 0 0 disallowed
J Q
0 1 0 1 0 1 1 0
clk
1 0 1 0 1 0 0 1
K Q 1 1 toggle 1 1 clocked

clocked logic direct logic
Clr

Figure 6-1. JK Flip-Flop Logic Symbol and Truth Tables

The first entry of the clocked truth table is the memory state, while the next
two combinations are the latched states. What is new with the JK flip-flop
is the fourth combination (1,1), which produces a toggle state. On clocking,
the output changes from [1-->0] if 1 or [0-->1] if 0. This complement
function is often referred to as bit toggling, and the resulting flip-flop (J and
K inputs pulled HI) is called a T flip-flop. Because only one toggle occurs
per output cycle, it takes two clock cycles to return the output state to its
initial state. Load Binary1.vi and observe the operation of the T-flip-flop on
clocking.


Lab 6 JK Master-Slave Flip-Flop

Figure 6-2. LabVIEW Simulation of a Divide-by-Two Counter Using a T Flip-Flop SubVI

Each time the Run button is pressed, the clock changes state from HI-LO or
LO-HI.

How many times do you need to press the Run button to cycle the output bit
from LO-HI-LO?

It may be easier to make the correct observation by pressing the Run
Continuously button. Because two clock pulses are required for the output
to cycle, the T flip-flop divides the clock frequency by two and is often
called a “divide-by-two” binary counter.

In LabVIEW (see the block diagram and open the T flip-flop subVI), the T
flip-flop is simulated with a Case structure placed inside a While Loop. The
upper shift register, with the inverter, simulates the digital clock.

If the output of one T flip-flop is used as the clock input for a second T
flip-flop, the output frequency of the pair of flip-flops is (/2 and /2) or divide
by 4. Load and run Binary2.vi.

Figure 6-3. LabVIEW Simulation of a Divide-by-Four Binary Counter

If the output of the first flip-flop is weighted as 1 and the second flip-flop
as 2, the decimal equivalent values during clocking form the sequence
0,1,2,3, 0,1,2,3, 0,1,2,3, etc. This is a modulo 4 binary counter. In the
LabVIEW simulation, note on the block diagram how the output of the first
flip-flop is ANDed with the clock to become the input of the next flip-flop.



Binary Counters
Binary counters are formed from J-K flip-flops by tying all the (J,K) inputs
to a logic 1 (HI) and connecting the output of each flip-flop to the clock of
the next flip-flop. The clock signal enters the chain at the clock of the first
flip-flop, and the result ripples down the chain.

Q0 Q1 Q2 Q3
Hi Hi Hi Hi

J Q J Q J Q J Q
clock C C C C
K Q K Q K Q K Q

Hi Hi Hi Hi

Figure 6-4. 4-Bit Binary Counter Built with JK Flip-Flops

In this configuration, the clock signal is divided by 2 each time it passes
through a JK flip-flop. Four JKs in sequence divide by 24 or 16.

Load the 4-bit binary VI called Binary4.vi, which simulates the above
binary counter. By pressing the Run button, observe the operation of the
divide-by-16 binary counter. The four binary states (Q3, Q2, Q1, Q0) are
displayed as LED indicators, and the decimal equivalent value as a numeric
on the front panel. In addition, the timing diagram is shown for the four
outputs Q0-Q3 on four separate charts.



Figure 6-5. LabVIEW Simulation of a 4-Bit Binary Counter

Observe the sequence and fill in the truth table below.

Table 6-1. 4-Bit Binary Count Sequence and Decimal Equivalent Values

Clock Cycle Q3 Q2 Q1 Q0 DE #
0 0 0 0 0 0
1
2
3
4
5
6
7
8
9
10
11
12
13
15
16 1 1 1 1 15



The complete table displays all binary combinations for a 4-bit binary
counter. If the outputs Q0, Q1, Q2, and Q3 are weighted as 20, 21, 22, and 23,
all the binary numbers 0-15 can be represented on the four outputs. Look at
the LabVIEW block diagram to see how the decimal equivalent value is
calculated.

In hexadecimal counting, the 16 states (0-15) are labeled as 0...9 and
A...F. This notation is more compact and easier to remember than long
combinations of binary bits. Larger bit lengths are subdivided into groups of
4 bits called a nibble, and each nibble is coded as one hexadecimal character.

For example, the 16-bit binary number 1101 0111 0011 1100 is coded as
$D73C hexadecimal.

8-Bit Binary Counter
A logical extension of the 4-bit binary counter is to higher data widths.
Embedded controllers use an internal 8-bit data bus, and modern
microprocessors use 16- or 32-bit data paths. The VI Binary8.vi
demonstrates visually the binary counting sequence as a byte on eight LED
indicators or as an 8-bit timing diagram. Run this VI continuously to
observe binary numbers from 0-255. The timing diagram clearly shows how
each stage divides the previous output by 2. The output frequencies are f/2,
f/4, f/8, f/16, f/32, f/64, f/128, and f/256 for the output stages Q0...Q7. Here,
f is the clock frequency.

Binary counters need to be reset (all bits 0) or set (all bits 1) for various
operations. The truth table for the JK flip-flop shown above has direct inputs
that provide this function. The clocked logic can occur whenever the reset
and set inputs are pulled high. A 0 on either the Set or Clear input forces the
output to a 1 or 0, respectively. These operations are exclusive, hence the
(00) state is disallowed. The VI Bin8_Reset.vi provides a clear function for
the 8-bit binary counter. Load and run this VI continuously. By pressing the
Reset button, the binary counter is cleared. This operation is useful in
applications for odd length counters and in designing analog-to-digital
converters.

LabVIEW Challenge
Design a two-digit binary counter, which counts from 00 to 99.

Summary
Binary counters are a fundamental component in digital electronic circuits.
They are used in all forms of modulo-n counters, in the generation of
harmonic clock subfrequencies, and in many higher order functions such as
digital-to-analog and analog-to-digital devices.



• Binary1.vi (Divide by 2 binary counter)
• Binary2.vi (Divide by 4 binary counter)
• Binary4.vi (Divide by 16 binary counter with logic traces)
• Binary8.vi (Divide by 256 binary counter with logic traces)
• Bin8_Reset.vi (8-bit binary counter with external reset button)
• FlipFlop.vi (T flip-flop subVI used in above programs)


Lab 7
Digital-to-Analog Converter

The digital-to-analog converter, known as the D/A converter (read as D-to-A
converter) or the DAC, is a major interface circuit that forms the bridge
between the analog and digital worlds. DACs are the core of many circuits
and instruments, including digital voltmeters, plotters, oscilloscope
displays, and many computer-controlled devices. This chapter examines the
digital-to-analog converter, several variations, and how it is used for
waveform generation.

What is a DAC?
A DAC is an electronic component that converts digital logic levels into an
analog voltage. The output of a DAC is just the sum of all the input bits
weighted in a particular manner:
DAC = ∑w b i i
i=0

where wi is a weighting factor, bi is the bit value (1 or 0), and i is the index
of the bit number. In the case of a binary weighting scheme, wi = 2i, the
complete expression for an 8-bit DAC is written as
DAC = 128 b7 + 64 b6 + 32 b5 + 16 b4 + 8 b3 + 4 b2 + 2 b1+ 1 b0


Lab 7 Digital-to-Analog Converter

Figure 7-1. LabVIEW Simulation of an 8-Bit DAC

The above simulation, DAC.vi demonstrates the conversion process. On the
front panel, eight Boolean switches set the input bits b0 through b7. Eight
LED indicators display the binary value of the input byte when the
simulation is run. The analog output is displayed as a numeric indicator. The
diagram panel displays the LabVIEW algorithm shown below for the 8-bit
converter.

Figure 7-2. LabVIEW VI for 8-Bit DAC.vi

The simulation uses two input multiply and add functions to generate the
DAC sum. Note the Boolean-to-Real icon on the block diagram, which



simulates in a very real way the bridging of the binary (Boolean levels) into
the analog (numeric) value.

Load and run DAC.vi to observe the relationship between the binary codes
and their numeric equivalent. DAC.vi is also a subVI, so it can be used in
other programs to convert any 8-bit digital signal into the decimal equivalent
value. To see how a DAC might be used, consider the simulation of an 8-bit
add instruction inside a microcomputer chip.

ALU Simulator
The arithmetic and logic unit (ALU) is responsible for all arithmetic and
logic operations occurring inside the central processing unit (CPU) of a
computer chip. Consider the add instruction
ADD R1,R2

which adds the contents of Register 1 with the contents of Register 2 and
stores the sum into an accumulator. Eight Boolean switches and displays
simulate the 8-bit registers R1 and R2. Nine LED indicators show the value
of the accumulator and any overflow in the carry bit. Three copies of
DAC.vi convert the contents of the three registers into their numeric
equivalent value.

Figure 7-3. LabVIEW Simulation of an 8-Bit Binary Adder

Load and run ADD R1,R2.vi to observe 8-bit binary addition in action. Try
adding simple sequences such as (1+1) to more complicated patterns such
as $EF +$3. Observe the operation of the carry bit. This VI can add larger
bit values such as 16-bit numbers. On the block diagram, you will see how
the binary addition modules of Lab 3 have been used with the DAC.vi
modules to complete the simulation.



Simulating a Real DAC Chip
The Motorola MC1408 is an 8-bit digital-to-analog converter that provides
an output current, i, directly proportional to the digital input. The transfer
function found in the DAC specifications is
i = K {A1/2+A2/4+A3/8+A4/16+A5/32+A6/64+A7/128+A8/256}

where the digital inputs Ai = 0 or 1, and here A1 is the most significant
bit. A8 is the least significant bit, and the proportionality constant
K = Vref / R14. The reference voltage taken here as +5 V supplies a
reference current of 5 V/3.9 kΩ, which equals 1.28 ma through the resister
R14. The maximum current produced when all input bits are high is
0.996 * 1.28 ma = 1.275 ma.

Vref(+5v)
VCC(+5v)
R14 2.0 kW
MSB 13 14
A1 5 (3.9 kW)
. 6
. 7 +15v
8 MC
9 4 – 7
1408 2
10
R15 6 Vout
. 11
15
741
A8 12
LSB (3.9 kW) +
3 4
16 3 2
15 pF –15v
VEE
(–15v)

Figure 7-4. 8-Bit DAC Circuit Built with Conventional Integrated Circuits

An operational amplifier, MC741, configured as a current-to-voltage
converter, converts the DAC current into a voltage, Vout = - iR. For a
feedback resistor of 2.0 kΩ, the maximum output is - 2.55 V, and the
sensitivity is 10 mV/bit. This is a convenient scaling constant, because the
maximum digital input, all bits high, has a decimal equivalent value of 255.



Figure 7-5. LabVIEW Simulation of the 8-Bit DAC Circuit Shown in Figure 7-4

Load and study the VI MC1408.vi, which simulates a DAC circuit using the
1408 DAC chip. Observe that the DAC resolution (that is, 1 bit change) is
10 mV. By adjusting the feedback resistor, the output can be scaled to any
convenient full scale value (for example, 1.000). Note the differences on this
block diagram as compared to the DAC.vi block diagram. If you have
access to an MC1408 DAC and 741 OpAmp, the simulation can be
compared with the real circuit shown in the schematic diagram.

Waveform Generators
Any sequence of bits fed to the inputs of the DAC at a uniform rate can be
used to produce an analog waveform. The simplest sequence is derived from
the outputs of an 8-bit binary counter. This will generate a 0-2.55 V digital
ramp waveform. For this demonstration, the VI Binary8.vi introduced in
Lab 5 is connected to DAC.vi. Its output is then connected to a waveform
chart. The slope of the ramp is set by the frequency of counts—the larger the
frequency, the larger the slope. An oscillator module generates the clock
signal. When the binary counter overflows from (11111111) to (00000000),
the analog voltage falls sharply from 255 to 0. This digital ramp is
sometimes called a staircase waveform, as it resembles a stairway.



Figure 7-6. Output of a 4-Bit, 6-Bit, and 8-Bit DAC

As the number of bits of the DAC increases, the height of the stair step
shrinks in size. A 4-bit DAC has 15 steps, a 6-bit DAC has 63 steps, and an
8-bit DAC has 255 steps. The above simulation, called DAC Resolution.vi,
demonstrates dynamically how the resolution is increased with bit width. In
the limit, as the number of bits increases from 16 to 20, the digital waveform
more closely approximates an analog ramp. In the analog world, such a
waveform is called a sawtooth wave. Take a look at the output of
DAC8/12.vi, which demonstrates the added resolution in moving from an
8-bit to a 12-bit DAC. Most engineering and scientific applications require
at least 12-bit resolution.

Special DACs
In unsigned binary arithmetic, all the numbers are positive. Signed
arithmetic uses the most significant bit to indicate the sign of the number
(0 is positive and 1 is negative). In this case, the 256 binary values of an 8-bit
DAC are divided into the positive numbers from 0 to 127 and negative
numbers from -128 to -1. The VI named DAC+/-.vi demonstrates a signed
analog output.



Figure 7-7. Unsigned and Signed DAC Output

Note that the range of Y is identical for both the signed and unsigned
version.

Lissajous Figures
If two signals are harmonically related, a plot of one on the x-axis against
the other on the y-axis yields interesting patterns called Lissajous figures.
By counting the number of intersection points a horizontal line makes with
the pattern and dividing by the number of intersection points a vertical line
makes with the pattern, you can find the ratio of the two frequencies. In the
following example, there are four intersection points on a horizontal line and
two on a vertical line, giving a ratio of 2:1. In addition, if the two signals are
perfect harmonics, the Lissajous pattern can also give the phase between the
two signals. Load Lissajous1.vi and investigate the phase relationship of
two harmonically related signals.

Figure 7-8. LabVIEW Simulation for a Lissajous Plot ω2=2*ω1



• DAC.vi (8-bit DAC simulation)
• ADD R1,R2.vi (8-bit binary adder)
• MC1408.vi (simulation of a Motorola 1408 DAC IC)
• DAC Resolution.vi (4-bit, 6-bit and 8-bit DAC simulation)
• DAC+/-.vi (unsigned and signed DACs)
• Lissajous.vi (simulation of a Lissajous plot)
• DAC8/12.vi (resolution of an 8-bit and a 12-bit DAC)
• DAC12.vi (subVI used in DAC8/12.vi)
• BIN_RST.vi (8-bit binary counter with reset)
• Half Adder.vi (subVI used in ADD R1,R2.vi)
• Full Adder.vi (subVI used in ADD R1,R2.vi)
• FlipFlop.vi (subVI used in ADD R1,R2.vi)


Lab 8
Analog-to-Digital Converters,
Part I

The analog-to-digital converter, known as the A/D converter (read as A-to-D
converter) or the ADC, is the second key component to bridging the analog
and digital worlds. The ADC is the basis of digital voltmeters, digital
multimeters, multichannel analyzers, oscilloscopes, and many other
instruments. There are many different ADC designs, of which the ramp,
tracking, and successive approximation converters are common. This lab
looks at the ramp and tracking A/D converters.

Purpose of the Analog-to-Digital Converter
The purpose of an ADC converter is to produce a digital binary number that
is proportional to an analog input signal. The fundamental conversion
process is shown in the following diagram.

Input Voltage +
C
–
Test Voltage

DAC

b7 b0
Reset
Counter

Figure 8-1. Symbolic Design for an 8-Bit Analog-to-Digital Converter

A counter creates a test binary sequence, and its digital output is converted
into an analog voltage using a digital-to-analog converter. The DAC is a
basic element of many ADC circuits and was discussed in Lab 7. (This is a
good time to review its operation if you are not familiar with the DAC.) The
test voltage is then compared with the input signal. If the input signal is
larger than the test signal, the counter is increased to bring the test signal
closer to the input level. If the input signal is smaller than the test signal, the
counter is decreased to bring the test signal closer to the input level. The


Lab 8 Analog-to-Digital Converters, Part I

process continues until the comparator changes sign, at which time the test
level will be within one count of the input level. Increasing the number of
bits of the counter and DAC increases the conversion resolution.

The Ramp ADC
The ramp ADC uses a binary counter and digital-to-analog converter to
generate a ramp test waveform. In this demonstration, an 8-bit binary up
counter, Binary Counter.vi, together with the 8-bit DAC, DAC.vi
(introduced in the last lab), generate the test waveform. The test level will
rise from 0 to 255 and repeat if left in the free running mode. However, when
the test level becomes greater than—or in this case, equal to—the input
level, the comparator will change sign and stop.

Figure 8-2. LabVIEW VI to Simulate an 8-Bit Ramp ADC

The last value on the binary bits (b7-b0) is the digitized value of the input
voltage level. In the LabVIEW simulation, a wait time of 60 ms is chosen so
that the eye can follow the action. The comparator function is simulated with
the LabVIEW Equal function.

Load and run the simulation VI Ramp.vi and follow the action on the front
panel. Try other values of the input level and note that the conversion time
depends on the input voltage level.



Figure 8-3. LabVIEW Front Panel of 8-Bit ADC Converter. The Comparator LED Indicator
Changes State When the Test Waveform Numeric Value Exceeds the Voltage Input

In the next simulation, Ramp4.vi, the binary counter is allowed to free run.
Whenever the test signal is greater than the input level, the comparator
changes sign. This intersection of the ramp waveform with the input level
can be seen on a chart display. The binary value of the counter at the
intersection point is the digitized signal. The transition of the comparator
indicates this event.

If the changing state of the comparator resets the binary counter, a true ramp
ADC is simulated. In this case, the binary counter is replaced with the binary
counter with reset, featured in Lab 6. Load the VI Ramp2.vi and observe
the action. Note that as soon as the test level reaches the input level, the
binary counter resets, and the ramp cycle starts all over again. In the display
below, the input level was changed three times.

Figure 8-4. Chart Display of the Ramp ADC in Operation

An interesting feature, unique to the ramp ADC, is that the conversion time
depends on the magnitude of the input signal. Small input levels are
digitized faster than large input levels. The conversion time is thus
dependent on the input signal magnitude and the clock circuitry speed. For
an 8-bit DAC, variable conversion times may not be a problem when the
clock is running at megahertz frequencies, but for 12-bit DACs, this
property is a disadvantage.



The ramp ADC works equally well with a down counter that runs from
255-0. The change of state of the comparator again signals the binary count
that generates a test level equal to the input level.

LabVIEW Challenge
Design a ramp ADC that uses a down counter to generate the test waveform.

Could you use an up/down counter to track the input level?

Yes, such a conversion technique is called a tracking ADC, and it has the
fastest conversion time.

Tracking ADC
The first task for the tracking ADC is to use some technique such as a ramp
waveform to catch up to the input level. At that point, shown by the
intersection of the ramp waveform with the input level, the tracking
algorithm takes over.

Figure 8-5. Tracking ADC Ramps Up to the Input Level Before Tracking Begins

The tracking algorithm is simply,
if
test level is greater than the signal level, decrease the count by one
else if
test level is less than the signal level, increase the count by one

and repeat forever.

In the following example, a positive ramp ADC technique is used to initially
catch up to the input level of 150.2. Once the input level is reached, the
tracking algorithm takes over.



By expanding the vertical scale, you can see the tracking algorithm in
action.

Figure 8-6. Tracking ADC Output when Input is Constant

However, if the input level changes, the ADC must revert to a ramp
waveform to catch up to the input level. Provided the clock is fast enough,
the tracking can keep pace. But if the signal changes too quickly, the
digitized signal is lost until the test level catches up again. In practice, it is
the slewing speed of the DAC that limits the maximum input frequency that
the tracking ADC can follow.

Figure 8-7. A Sudden Change in the Input Level Causes
the Test Level to Ramp Up to the New Level

Because the tracking ADC uses an up/down counter, the algorithm has the
same problem when the input signal suddenly falls below the test level. The
tracking ADC reverts to a down ramp (Figure 8-8) until the test level reaches
the input signal level.



Figure 8-8. A Negative Change in the Input Level Causes
the Test Level to Ramp Down to the New Level

The VI called Tracking ADC.vi is used to demonstrate this technique and
to generate all the above charts. The algorithm shown on the block diagram
is quite simple. A LabVIEW Select function and the shift register on the
While Loop implements the algorithm.

Figure 8-9. LabVIEW VI for the Tracking ADC

The Wait function is set to 0.10 second so that the user can observe the
action on the front panel. You can also use the Operating tool to redefine the
vertical axis scale to zoom in on the action as the simulation is in progress.
To observe the tracker catching up to a varying input, reduce the input
constant for the Wait function in Figure 8-9 to 1 ms.

• Ramp.vi (8-bit ramp ADC, conversion slowed for easy viewing)
• Ramp4.vi (ramp ADC with no feedback from comparator)
• Ramp2.vi (8-bit ramp ADC with chart output)
• Tracking ADC1.vi
• Binary Counter.vi (subVI 8-bit binary counter)
• BIN_RST.vi (subVI 8-bit binary counter with external reset)
• DAC.vi (subVI 8-bit DAC)
• FlipFlop.vi (subVI)


Lab 9
Analog-to-Digital Converters,
Part II

In the last lab, binary counters in the form of up and up/down counters were
used to create test waveforms for ramp and tracking ADCs. Another popular
ADC is based on a test waveform created from a successive approximation
register (SAR). These ADCs are substantially faster than the ramp ADCs
and have a constant and known conversion time. SARs make use of the
binary weighting scheme by outputting each bit in succession from the most
significant bit (MSB) to the least significant bit (LSB).

The SAR algorithm is as follows:
1. Reset the SAR register and set the DAC to zero.
2. Set MSB of SAR:
if VDAC is greater than Vin, then turn that bit off.
else if VDAC is less than Vin, leave the bit on.
3. Repeat step 2 for the next MSB, until all n bits of the SAR have been
set and tested.
4. After n cycles, the digital output of the SAR will contain the
digitized value of the input signal.

This algorithm can best be seen with the aid of a graph of the input signal
level and the DAC waveform produced by the SAR. Suppose a value of 153
is input into the ADC circuit. The number 153 is 128 + 16 + 8 + 1. In binary,
reading right to left, the number is
15310 = (10011001)2

The SAR algorithm states that the MSB, having the value of 128, is to be
tested first. Because 128 is less than 153, the MSB is to be kept. The best
estimate after the first cycle is (1000 0000). On the next cycle, the next
MSB, having value 64, is added to the best estimate (that is, 128 + 64 = 192).
Because 192 is greater than 153, this bit is not kept, and the best estimate
remains (1000 0000). In the following cycle, the next bit value of 32 yields
a test value of 128 + 32 = 160. Again, the test value is greater than the input


Lab 9 Analog-to-Digital Converters, Part II

level, so this bit is not kept, and the best estimate remains at (1000 0000). In
the following cycle, the next test value of 16 yields 128 + 16 = 144. This
value is less than 153, so this bit is kept. After 4 cycles, the best estimate is
(1001 0000). The remaining cycles can be seen on the LabVIEW simulation
for a successive approximation analog-to-digital converter.

In the panel below, the timing diagram shows precisely this process. The
solid line is the test value for each cycle, and the dashed line is the input level
of 153. Continuing for the next four cycles yields the final binary value
displayed on eight LED indicators.

Figure 9-1. Successive Approximation Waveform Used to Digitize Input Voltage

Load the VI named SAR.vi and run the VI in the continuous mode. You
can use the Operating tool to change the input level, and the SAR test
waveform will dutifully follow, digitizing the input level in all cases in the
same 8 cycles. The DAC output MSB settling time sets the fundamental
speed limitation. Most ADCs based on SARs have conversion times of less
than 100 ms.

Figure 9-2. Digitized Value of an SAR ADC Displayed as a Boolean Array



A second VI, SAR0.vi, slows the action so you can watch each cycle. The
input level is set to 153. The test level is the DAC output, with each bit value
added to the previous best estimate as discussed above. The digitized value
is the best estimate of the input level after 8 cycles. The Boolean array of
indicators shows the binary value of the best estimate as it is developed, and
after the 8 cycles, the array contains the digitized value.

SAR Simulation
The LabVIEW simulation is somewhat complex, as is a real SAR chip. As
a result, the SAR0.vi block diagram will be discussed in two parts—first,
the SAR algorithm, and then the binary representation using a Boolean
array.

The test bit is formed by taking the number 256 and successively dividing it
by two in a shift register eight times. The sequence at the Bit Value will read
(128, 64, 32,16, 8, 4, 2, and 1) as the loop counter cycles from 0 to 7. The
ninth loop is needed to load the initial values into the shift registers. The test
value is formed by adding the new bit value to the previous best estimate.
The compare function decides whether the current bit should be included in
the new best value. After the 8 cycles of the SAR, the best value is the
digitized level.

Figure 9-3. LabVIEW Simulation of the SAR Algorithm Using Shift Registers

To generate a binary representation of the best estimate, a Boolean
accumulator in the form of a Boolean shift register is used. The Test Bit,
either a high or low, is passed in the array after each cycle using the
LabVIEW Replace Array Element function. The Boolean True or False is
loaded into the Boolean array at the index specified by the loop counter.
Initially, the eight-element array is set to Boolean False states to ensure that
all LED indicators in the Boolean array are off.



Figure 9-4. LabVIEW Simulation of SAR Using Arrays

As the best estimate is built, the digitized binary value shows up on the front
panel. After the 8 cycles, the binary value is complete, and its decimal
equivalent is identical to the digitized value shown in the numeric display.

The LabVIEW string function Format and Strip formats any string input
into a number according to the selected conversion code. In SAR_Hex.vi, a
two-character string representing a hexadecimal number from $00 to $FF is
converted into a numeric from 0 to 255 and digitized using the SAR
algorithm with arrays. Try running this VI.

Summary
In the last two labs, three types of analog-to-digital converters were
introduced and demonstrated. The ramp ADC is conceptually the simplest,
but suffers from a variable conversion time proportional to the input signal
magnitude. The tracking ADC is the fastest converter, as long as no rapid
changes in the input signal level occur. The overall best choice is the
successive approximation ADC, with a constant and known conversion
time.

• SAR.vi (successive approximation register ADC)
• SAR0.vi (SAR ADC slow version for observing the conversion process)
• SAR_Hex.vi (SAR ADC with a hexadecimal input)


Lab 10
Seven-Segment Digital
Displays

Digital displays link the digital world of ones and zeros with numerics of the
human world. You have seen how parallel combinations of ones and zeros
can represent binary, hexadecimal, or digital numbers. For most simple
instruments, digital displays use the numbers 0-9 and are represented by
seven segmented displays. Each segment is controlled by a single bit, and
combinations of segments turned ON or OFF can display all the numbers
0-9 and a few characters, such as A, b, c, d, E, and F.

Seven-Segment Display
The LED seven-segment display uses seven individual light emitting diodes,
configured as the number 8 in the pattern shown below:

a
f
b

g
e
c
d

Figure 10-1. Seven-Segment Display Uses Seven LED Bars

The individual segments are coded a, b, c, d, e, f, and g and are ordered
clockwise, with the last segment (g) as the central bar. When an LED is
forward biased, light is emitted. By shaping the LED as a horizontal or
vertical bar, a segment can be formed. Many output devices such as
computer parallel ports are 8 bits wide. An eighth diode in the shape of a dot
is available on some seven-segment displays to indicate a decimal point.


Lab 10 Seven-Segment Digital Displays

Run the VI 7 Segment.vi, which is a LabVIEW simulation for a
seven-segment display. Try different combinations of the switches.

How many characters in the alphabet can you display?

Figure 10-2. LabVIEW Simulation of a Seven-Segment Display

The input bits 0-7 are represented by eight Boolean switches. The
corresponding segments in the seven-segment display are traditionally
labeled a to g and dp (decimal place). The least significant bit 0 is wired to
segment a, the next bit 1 is wired to segment b, etc. The most significant port
bit, bit 7, is often wired to an eighth LED and used as a decimal point. By
operating the switches, you can display all the numbers and a few
characters. After experimenting with the display, try outputting the message
“help call 911” one character at a time.

Most seven-segment displays are driven with an encoder that converts a
binary encoded nibble into a numeric number, which in turn selects the
appropriate seven-segment code. The first step in a LabVIEW simulation is
to convert the 4-bit binary nibble into a number from 0 to 15. The VI named
Bin->Digit.vi simulates this task.

Figure 10-3. Front Panel of the 4-Bit Binary-to-Digit Conversion Program



On the block diagram, a 4-bit digital-to-analog converter completes the
operation.

Figure 10-4. LabVIEW VI for a 4-Bit Digital-to Analog Converter

The next step is to convert the digit(s) 0 to 15 into the appropriate
seven-segment display. For the numbers 10 to 15, a single hexadecimal
character [A to F] is used. In Encoder Hex.vi, multiple case statements are
used to provide the encoder function. The Case terminal ? is wired to a
numeric control formatted to select a single integer character. The number 0
outputs the seven-segment code for zero, number 1 outputs the code for 1,
etc., all the way to F. The Boolean constants inside each Case statement are
initialized to generate the correct seven-segment code.

Figure 10-5. LabVIEW VI for Numeric-to-Seven-Segment Display

The hexadecimal number inside the square box is the hexadecimal
representation for the 8-bit pattern necessary to represent the number, #n.

Each port has a unique address that must be selected before data can be
written to or read from the real world. The correct address must be entered



on the front panel to access the port. In this simulation, the address operates
the run command.

Figure 10-6. Hexadecimal-to-Seven-Segment Display Encoder and Indicator

Select the port address 1 and run Encoder.vi. With the Operating tool, click
on the slider and drag it along the range of numbers, 0 to 15. You can see all
numbers encoded as a seven-segment hexadecimal character.

These two VIs, Bin->Digit.vi and Encoder.vi, can be combined to form a
binary-to-seven-segment encoder and display.

16 7
4 16
segment
binary line
encoder
encoder
driver

Figure 10-7. Symbolic Diagram of a Binary-to-Seven-Segment Display Circuit

In general, the input would be a 4-bit binary number and the output would
be the seven-segment code for the binary bit pattern. First, the 4-bit binary
nibble is converted to one of 16 outputs. These outputs then select the
appropriate seven-segment code. Finally, these outputs are passed to a
seven-segment display. Load and run the VI Display7.vi, which emulates
this operation.



Figure 10-8. Binary-to-Seven-Segment Front Panel

LabVIEW Challenge
Design a two-digit counter that counts from 0 to 99. Use the 8-bit binary
counter from Lab 6 modified to count in decimal.

• 7Segment.vi (LabVIEW simulation of a seven-segment display)
• Bin->Digit.vi (4-bit digital-to-analog converter)
• Encoder Hex.vi (seven-segment display, hexadecimal version)
• Display7.vi (hexadecimal encoded binary-to-seven-segment display)



Notes


Lab 11
Serial Communications

Many instruments, controllers, and computers are equipped with a serial
interface. The ability to communicate to these devices over a serial interface
opens a whole new world of measurement and control. The standard bit
serial format, RS-232, defines the bit order and waveform shape in both time
and amplitude. At a minimum, only three communication lines are needed
for communication between a computer and an external device: transmit,
receive, and a reference ground.

Transmit Line
Receive Line
Ground Line

Figure 11-1. Serial Communication Lines

In serial communications, a high level is called a Mark state, while the low
level is called the Space state. In normal operation, the output line is in a
high state, often denoted as a 1, or in LabVIEW as a Boolean True. The
transmitter signals the receiver that it is about to send data by pulling the
transmit line low to the space state (0). This falling edge or negative
transition is the signal for the receiver to get ready for incoming data. In
RS-232 communication, all data bits are sent and held for a constant period
of time. This timing period is the reciprocal of the Baud rate, the frequency
of data transmission measured in bits per second. For example, a 300 Baud
data rate has a timing period of 1/300 of a second or 3.33 ms. At the start of
each timing period, the output line is pulled high or low and then held in that
state for the timing period. Together, these transitions and levels form a
serial waveform.

Consider an 8-bit data byte $3A (or in binary, (0011 1010)). For serial
communication, the protocol demands that the least significant bit, b0, be
transmitted first and the most significant bit, b7, last. By convention, time is
represented as moving from left to right, hence the above data byte would
be transmitted as (01011100), in reverse order.


Lab 11 Serial Communications

b0 b7
8-bit data
$3A 0 1 0 1 1 1 0 0

Figure 11-2. Serial Transmitter Sends the LSB (b0) First

The protocol also requires that the data byte be framed by two special bits,
the start bit (Space state) and the Stop bit (Mark state).

Start b0 b7 Stop
0 0 1 0 1 1 1 0 0 1
bit data byte $3A bit

Figure 11-3. Handshaking Bits Start and Stop Frame the Data Byte

The addition of these framing bits requires 10 timing periods to send one
data byte. If each byte represents one ASCII character, 10 serial bits are sent
for each character. For example, a 9600 Baud modem is capable of sending
960 characters per second. In terms of a timing diagram, the RS-232 serial
waveform for the $3A data byte looks like the following.

b0 b7
Start 0 0 1 0 1 1 1 0 0 1 Stop

Figure 11-4. Serial Waveform for a $3A Data Byte

Serial Transmitter
In LabVIEW, a serial transmitter can be designed using a 10-bit shift register
and a delay loop that simulates the Baud rate. Launch the VI Serial.vi.

Figure 11-5. LabVIEW Simulation of a Serial Transmitter

On the front panel, you can load the date byte into the shift register by
operating the eight input switches. Note that the bit order in hexadecimal
places the most significant bit on the left. Hence, $33 is entered as (0011
0011). However, the data comes out in the reverse order, with the least



significant bit first. The serial output is displayed on the large square LED
indicator. Initially, it is in the Mark state. All data bits and framing bits are
shown as zeros before execution. As soon as the run button is pressed, $33
is loaded into the shift register, the stop bit becomes a 1, and the start bit
becomes a 0. The output bit immediately falls to the off state, signaling the
start of transmission. After a delay (1/Baud Rate), the next bit is output.
The diagram panel displays the transmitter algorithm.

Figure 11-6. LabVIEW Diagram Panel for the Serial Transmitter Simulation
The first bit to be output (Start) is initialized to the Space state (0), a Boolean
False. The following eight elements are the data byte in sequence, least
significant bit to most significant bit. The last element on the shift register
(Stop bit) is initialized to a Mark state (1), a Boolean True. The VI, when
called, executes the loop 10 times. Each loop outputs one serial bit. A wait
structure simulates the “basic timing period” or 1/Baud Rate.
As the data is shifted out the serial line, the shift register is filled with ones.
This ensures the output will be in the Mark state at the end of transmission,
after 10 cycles.

Figure 11-7. Transmitter Buffer After Data Byte Has Been Sent to the Port

It becomes easier to view the serial waveforms by writing the serial output
to an oscilloscope or a strip chart recorder. In the second VI, Serial1.vi, the
serial output is converted into a numeric and then written to a LabVIEW



chart. By selecting the correct set of chart symbols and interpolation
features, the trace will resemble that of an oscilloscope trace, and you can
view the transmitted serial waveforms at low baud rates.

The following traces show the waveforms for the numbers $00 (00000000),
$55 (01010101), and $FF (11111111).

Figure 11-8. Serial Waveforms for Repetitive Transmission of the Same Data Byte

Note the middle case, $55, generates a square wave on the serial output pin.

Once built, the parallel-to-serial converter can be saved as a subVI and used
in other programs. In general, this VI will have eight binary inputs for the
input parallel data byte, a binary output for the serial bit stream, and a
numeric array for the logic trace.

Voltage to Serial Transmitter
In the first application, a numeric input simulates an analog input. The
numeric value has been conditioned to be in the range 0-255. RampADC.vi,
discussed in Lab 9, converts the analog signal into an 8-bit binary number,
which in turn is passed on to the parallel-to-serial converter. To observe the
signal, the serial waveform is passed into an array and presented on the front
panel as a logic trace.



Figure 11-9. Serial Transmitter Exploits LabVIEW SubVIs

Load the VI named V->Serial.vi and observe the serial waveforms. Each
number from 0 to 255 will yield a different waveform. Try the data bytes
$00, $55, and $FF to verify the waveforms shown in Figure 11-8.

In the second example, a two-character hexadecimal-encoded ASCII string
is input into a subVI named Hex->Numeric.vi, which converts the
hexadecimal characters into a number.

Figure 11-10. Waveform Generator with Hexadecimal Input

The hexadecimal string value is converted into a numeric value using a
LabVIEW string function called Format and Strip. The numeric value is
then passed on to the previous VI, V->Serial.vi, and displayed. Recall that
(0101 0101) in Serial1.vi generated a square wave. In HEX->Serial.vi, $55
also generates the square wave.

LabVIEW Challenge
Can you generalize this input to be any 7-bit ASCII character? The eighth
bit could be a parity bit, even or odd.

• Serial.vi (demonstration of a serial transmitter)
• Serial1.vi (Serial.vi with a logic trace output)
• V->Serial.vi (LabVIEW simulation of a serial transmitter)



• Hex->Serial.vi (LabVIEW simulation of a serial transmitter with hex
input)
• RampADC.vi (subVI 8-bit ADC)
• Binary Counter.vi (subVI 8-bit binary counter)
• DAC.vi (subVI 8-bit DAC)
• FlipFlop.vi (subVI T flip-flop)
• Hex->Numeric.vi (subVI that converts hexadecimal number into a
numeric)
• Serial2.vi (subVI Serial1.vi with numeric array output)


Lab 12
Central Processing Unit

The heart of any computer is the central processing unit (CPU). The CPU
communicates with the memory over a bidirectional data bus. In memory
reside program instructions, data constants, and variables, all placed in an
ordered sequence. The CPU reaches out to this sequence by controlling and
manipulating the address bus. Special memory locations called input/output
(I/O) ports pass binary information to or from the real world in the form of
parallel or serial data bytes. The system clock oversees the whole network
of gates, latches, and registers, ensuring that all bits arrive on time at the
right place and that no data trains collide. Of the four parts of a computer
(CPU, memory, I/O, and clock), the most important part is the CPU.

The CPU consists of several subgroups, including the arithmetic and logic
unit (ALU), the instruction decoder, the program counter, and a bank of
internal memory cells called registers. In a typical CPU sequence, the
program counter reaches out to the memory via the address bus to retrieve
the next instruction. This instruction is passed over the data bus to the
internal registers. The first part of the instruction is passed to the instruction
decoder. It decides which data paths must be opened and closed to execute
the instruction. In some cases, all the information needed to complete the
operation is embedded within the instruction. An example of this type of
instruction is “clear the accumulator.” In other cases, the instruction needs
additional information, and it returns to memory for the added data. An
example of this type of instruction might be “load Register 2 with the data
constant 5.” Once all the information is in place, the instruction is executed
by opening and closing various gates to allow execution of the instruction.

Typical instructions available to all CPUs include simple instructions with
data already inside the CPU, such as clear, complement, or increment the
accumulator. More complex instructions use two internal registers or data
coming from memory. This lab illustrates how the CPU executes simple and
a few complex operations using basic logic functions.


Lab 12 Central Processing Unit

Operation of the Arithmetic and Logic Unit
The arithmetic and logic unit (ALU) is a set of programmable two-input
logic gates that operate on parallel bit data of width 4, 8, 16, or 32 bits. This
lab will focus on 8-bit CPUs. The input registers will be called Register 1
and Register 2, and for simplicity the results of an operation will be placed
in a third register called Output. The type of instruction (AND, OR, or XOR)
is selected from the instruction mnemonic such as AND R1,R2.

Figure 12-1. LabVIEW Simulation of an Arithmetic and Logic Unit

In the LabVIEW simulation, ALU0.vi, the registers R1 and R2 are
represented by 1D arrays having Boolean controls for inputs. The output
register is a Boolean array of indicators. The function (AND, OR, or XOR)
is selected with the slide bar control. Data is entered into the input registers
by clicking on the bar below each bit. Running the program executes the
selected logic function.

The following are some elementary CPU operations.

What operation does AND R1[$00], R2[$XX]
OR R1[$FF], R2[$XX]
or XOR R1[$55], R2[$FF] represent?

In each case, the data to be entered is included inside the [ ] brackets as a
hexadecimal number such as $F3. Here, X is used to indicate any
hexadecimal character. Investigate the above operations using ALU0.vi.

The AND operation resets the output register to all zeroes, hence this
operation is equivalent to CLEAR OUTPUT. The OR operation sets all bits
high in the output register, hence this operation is equivalent to SET
OUTPUT. The third operation inverts the bits in R1, hence this operation is
equivalent to COMPLEMENT Register 1.



Consider the operation “Load the Output Register with the contents
contained in R1.” In a text-based programming language, this operation
might read “Output = Register 1.” Set R1 in ALU0.vi to some known value
and execute the operation AND R1,R2[$FF].

Another interesting combination, XOR R1,R1, provides another common
task, CLEAR R1. It should now be clear from these few examples that many
CPU operations that have specific meaning within a software context are
executed within the CPU using the basic gates introduced in Lab 1.

The Accumulator
In ALU0.vi, CPU operations are executed by stripping off one bit at a time
using the Index Array function, then executing the ALU operation on that
bit. The result is passed on to the output array at the same index with
Replace Array Element. After eight loops, each bit (0...7) has passed
through the ALU, and the CPU operation is complete.

Figure 12-2. LabVIEW VI to Simulate the Operation of an 8-Bit ALU

In LabVIEW, it is not necessary to strip off each bit, as this task can be done
automatically by disabling indexing at the For Loop tunnels. Array data
paths are thick lines, but become thin lines for a single data path inside the
loop. Study carefully the following example, which uses this LabVIEW
feature.

In many CPUs, the second input register, R2, is connected to the output
register so that the output becomes the input for the next operation. This
structure provides a much-simplified CPU structure, but more importantly,
the output register automatically becomes an accumulator.



Figure 12-3. ALU Simulation Uses the Auto Indexing at the For Loop Tunnels

In ALU1.vi, the previous accumulator value is input on the left, and the next
accumulator value is output on the right. This programming style allows
individual CPU instructions to be executed in sequence. Look at the
following example, Load A with 5 then Complement A.

Figure 12-4. LabVIEW VI to Load A with 5 Then Complement A

The first instruction, Load A with 5, is accomplished with the AND function
and a mask of (1111 1111). The binary value for 5 (0000 0101) is placed into
the initialization register, and the mask $FF into R1. ANDing these registers
loads R1 with 5 and places its value into the accumulator. Complement is
the XOR function with a mask of $FF. Load and run the VI, Prgm1.vi,
to see the operations. The complement of A appears in the label
Accumulator*.

Addition
The ALU not only executes logic operations, but also the arithmetic
operations. Recall from Lab 3 that binary addition adds the individual bits
using the XOR function and calculates any carry with an AND function.
Together, these two functions can be wired as a half adder (that is, bit 1 + bit
2 = a sum + a carry (if any)). To propagate bit addition to the next bit place,
a full adder is used, which sums the two input bits plus any carry from the
previous bit place. The VI named ADD_c.vi adds addition to the ALU
operations. The full adder shown below adds the two input bits plus a
previous carry using the Boolean shift register. A new instruction,



{ADD +1,A}, can now be added to the list of operations and added to the
Case structure.

Figure 12-5. ALU Operation: ADD with Carry

Binary Counter
Consider a software program to generate the binary patterns of an 8-bit
binary counter. It might be coded as “after clearing the accumulator, add one
to the accumulator again and again” for n times.

In a linear programming language, the program might read

Start CLEAR A : reset all bits in the accumulator to zero
Loop INCA : add +1 to accumulator
REPEAT Loop N : repeat last instruction n times

ANDing a register with $00 will reset that register, CLEAR A. In the CPU
list of instructions, the AND operation is case number 1. INC A is the ADD
+1,A instruction, CPU operation number 3. The simulation VI is shown
below.

Figure 12-6. LabVIEW VI of an 8-Bit Binary Counter

Note that the carry has not been wired. The INCREMENT instruction does
not affect the carry. By wiring the carry, the instruction would correctly be



written as ADD +1,A. Load and run the simulation VI, Prgm2.vi, and watch
yet again the binary counter. A Wait loop has been added so that the user can
easily see the action as the VI is run.

Figure 12-7. Front Panel for a LabVIEW Simulation of an 8-Bit Binary Counter

LabVIEW Challenge
Design a LabVIEW program to simulate the addition of two 16-bit numbers.

• ALU0.vi (LabVIEW simulation arithmetic and logic unit, AND, OR,
and XOR)
• ALU1.vi (ALU simulation with concise programming format)
• ADD_c.vi (ALU simulation with AND,OR, XOR, and ADD
operations)
• Prgm1.vi (LabVIEW CPU simulation: load A with 5, complement A)
• Prgm2.vi (LabVIEW CPU simulation of a binary counter: clear A,
ADD 1 to A)
• Half Adder.vi (subVI used in CPU add operation)
• Full Adder.vi (subVI used in CPU add operation)


Documentation Comment Form
National Instruments encourages you to comment on the documentation supplied with our products. This information
helps us provide quality products to meet your needs.
Title: Principles of Digital Electronics
Edition Date: March 1998
Part Number: 321948A-01

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