about digital logic circuit in DP&CO

1. Digital Principles and
Computer Organization
Unit – II
Digital Logic Circuits
Submitted by,
M. Kavitha,
M. Sc(CS&IT),
Nadar Saraswathi College of
Arts and Science,
Theni. 1

2. Digital Principle and Computer
Organization
Contents :
1. Logic Gates.
2. Boolean Algebra
3. Map Simplification.
4. Combinational Circuit.
5. Flip Flop.
6. Sequential Circuit.
2

3. 3
Logic Gates
* A logic gate is an electronic circuit which
makes logical decisions, the most common logic
gates are AND, OR, NOT gates.
* The NAND and NOR gates are called as the
Universal gates.
* The exclusive OR gates is another logic gate
which can be constructed using basic gates such as
AND, OR, NOT.
* There are more type of logic gates.

4. 4
Logic Gates :
* OR Gate.
* AND Gate.
* NOT Gate.
* NAND Gate.
* NOR Gate.
* Exclusive-OR(Ex-OR) Gate.

5. 5
OR Gate :
* The OR gate performs Logic addition,
it is known as OR function.
* The OR gate has two or more inputs
and only one output.
Y = A+B
The OR function can be expressed as
Y = A+B+C+D+……..

6. 6
A
B
Y=A+B
Input Output
Y= A+B
A B
0 0 0
0 1 1
1 0 1
1 1 1
a) Logic Symbol
b) OR gate truth table

7. 7
AND Gates :
* The AND gate performs logical
multiplication, it is known as AND
function.
* The AND gate has two or more input
and a single output.
Y= A . B
* Where the dot(.) denotes the AND
operation.
Y =AB

8. 8
A
B
Y=AB
Input Output
Y= AB
A B
0 0 0
0 1 0
1 0 0
1 1 1
a) Logic Symbol
b) AND gate truth table

9. 9
NOT gate :
* The NOT gate performs the basic
logical function called inversion or
complementation.
* The purpose of the gate is to convert
one logic level into the opposite logic level.
Input
A
Output
Y = A
0 1
1 0
Y= A
A
a) Logic Symbol
b) NOT gate truth table

10. 10
NAND gate :
* NAND is a contraction of the NOT-AND
gates.
* It has two or more inputs and only one
output.
10
Input Output
Y= AB
A B
0 0 1
0 1 1
1 0 1
1 1 0a) Logic Symbol
b) NAND gate truth table
A
B
Y=AB

11. 11
NOR gate :
* NOR is a contraction of NOT-OR
gates.
* It has two or more inputs and only
one output.
A
B
Y=A+B
Input Output
Y= A+B
A B
0 0 1
0 1 0
1 0 0
1 1 0a) Logic Symbol
b) NOR gate truth table

12. 12
Exclusive-OR(Ex-OR) gate :
* An Exclusive-OR gate is a gate with
two or more inputs and one output.
* The output of a two-input Ex-OR gate
a HIGH state.
Y=A
B
Input Output
Y= A B
A B
0 0 0
0 1 1
1 0 1
1 1 0a) Logic Symbol
b) Ex-OR gate truth table
+
+

13. Boolean Algebra
* Boolean Algebra , elements have one
of two values –True or False.
* The circuits in a computer are also
designed for two-state operations.
* That is input and output of a circuit is
either low(0) or high(1).
* The circuits are called logic circuits.
13

14. Boolean Algebra :
There are three basic operators in
Boolean Algebra which are called logical
operators or Boolean operators.
1. OR - logical addition
2. AND – logical multiplication
3. NOT – Logical negation
The Boolean operators are used to
combine Boolean variables and Boolean
constants to form Boolean Expressions.
14

15. 15
OR Operation
AND Operation

16. 16
NOT Operation
DeMorgan’s law :
1. (A.B)’= A’+ B’
2. (A+B)’= A’. B’

17. 17
Boolean Algebra
• The sum-of-products form
for our function is:
We note that this function is not in
simplest terms. Our aim is only to
rewrite our function in canonical
sum-of-products form.

18. 18
Map Simplification
K – Map Simplification :
K-map method can also be used for
simplifying the logic expression for s and c-
out.
0 1 0 1
1 0 1 0
0 0 1 0
0 1 1 1
AB
AB C out
C out 00 01 11 10
00 01 11 10
0
1
0
1
a) K-map for Sum
b) K-map for C out

19. 19
0 1
2 3
A
B
0
B
1A
1
Two variable k-map Three variable
0 1 3 2
4 5 7 6
A
BC
00 01 11 10
0
1
B
A
C
Four Variable k-map
0 1 3 2
4 5 7 6
12 13 15 14
8 9 11 10
AB
CD
00
01
11
10
00 01 11 10
A
B
C

20. Example for k – Map :
Product of sum simplification
Formula : F’ = AB+CD+BD’
F = (A’+B’)(C’+D’)(B’+D)
20
1 1 0 1
0 1 0 0
0 0 0 0
1 1 0 1

21. 21
Combinational Circuits
Combinational logic circuits are circuits in
which the output at any time depends upon the
combination of the input signals.
* Multiplexers
* De-Multiplexers
* Encoders
* Decoders

22. 22
Multiplexers (Data Selectors)
* The term ‘multiplex’ means “many into one”.
Multiplexing is the process of transmitting a large number of
information over a single line.
* A digital multiplexer is a combinational circuit that
selects one digital information from several source and
transmits the selected information on a single output line.
* A multiplexer is also called a data selector.
Multiplexer
1 output
signal
m select signals
n input
signal

23. 23
De-multiplexers(Data Distributors)
* The “demultiplex” means “one into many”.
* Demultiplexing is the process of taking information
from one input and transmitting the same over one of several
output.
* A demultiplexer is a logic circuit the receives
information on a single input and transmits the same
information over one for several (2n) output lines.
Demultiplexer 1 output
signal
m select signals
n input
signal

24. 24
Encoders
* An encoder is a digital circuit that performs the
inverse operation of a decoder and the opposite of the
decoding process is called encoding.
* Encoder is a combinational logic circuit that convert
an active input signal into a coded output signal.
Encoders
m outputs
n input

25. 25
Octal-to-Binary Encoder :
It is well-known that a binary-to-octal decoder a 3-
bit input code and activates one of eight output lines
corresponding to that code.
.
Input Output
D0 D1 D2 D3 D4 D5 D6 D7 Y2 Y1 Y0
1 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 1
0 0 1 0 0 0 0 0 0 1 0
0 0 0 1 0 0 0 0 0 1 1
0 0 0 0 1 0 0 0 1 0 0
0 0 0 0 0 1 0 0 1 0 1
0 0 0 0 0 0 1 0 1 1 0
0 0 0 0 0 0 0 1 1 1 1

26. 26
* An decoder is similar to demultiplexer but
without any data input. It is most digital systems
require the decoding of data.
* Decoding is necessary in applications such
as data demultiplexing, digital display, digital-to-
analog converters and memory addressing.
* Each output line will be activated for only
one of the possible combinations of inputs.
* A decoder is a number of output is greater
than the number of inputs.
Decoders

27. 3-to-8 Decoder :
A 3-to-8 decoder has three input (A,B,C) and
eight output(D0 to D7) based on 3 input one of the
eight output is selected.
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Input Output
A B C D0 D1 D2 D3 D4 D5 D6 D7
0 0 0 1 0 0 0 0 0 0 0
0 0 1 0 1 0 0 0 0 0 0
0 1 0 0 0 1 0 0 0 0 0
0 1 1 0 0 0 1 0 0 0 0
1 0 0 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 0 1 0 0
1 1 0 0 0 0 0 0 0 1 0
1 1 1 0 0 0 0 0 0 0 1

28. Flip Flops
* The simplest kind of sequential circuit
is a memory cell that has only two states it
is called flip flop.
* It is used to store One bit of
information with a 0 or a 1.
* A flip flop is also known as bistable,
multivibrator, latch or toggle.
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29. 29
Type of flip flop :
* Flip flop are of different types
depending on the input and clock pulses
cause transition between two states.
* There are four type of flip flop.
* S-R Flip flop (Set/Reset).
* D Flip flop (Delay/Data).
* J-K Flip flop.
* T Flip flop (Toggle).

30. S – R Flip Flop (SET/RESET)
30

31. 31

32. 32
Working of S – R Flip Flop (Set/Reset) :
* If both S and R are 0 during transition, the
output does not change.
* If S= 1 and R= 0, the out put Q is set to 1.
* If S= 0 and R=1, the output is cleared or reset
to 0.
* If both S and R are 1, the output is
unpredictable. This condition makes the RS flip flop
difficult to manage and therefore is forbidden in
practice.

33. D - Flip Flop (DELAY/DATA)
33

34. 34

35. Working of D – Flip Flop :
The D input goes directly into the S
input and the complement of the D input
goes to the R input.
* If it is 1, the flip-flop is switched
to the set state (unless it was already set).
* If it is 0, the flip-flop switches to
the clear state.
Applications:
1. Registers as storage devices.
2. Used as a Buffer. 3. In Digital system. 35

36. JK - Flip Flop (DELAY/DATA)
36

37. 37

38. Working of JK – Flip Flop :
* When j and k both are 0, the data
inputs have no effect on the outputs.
* When j=0 and k=1, the flip flop is
reset or cleared to 0.
* When j=1 and k=0. the flip flop is set
to 1.
* When j and k are 1, if the state of flip
flop was 0,applying a clock with 1and flip
flop state was 1, it changes to 0.
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39. * This on off state is TOGGLING.
* Racing condition: Toggling between
0 to 1 and 1 to 0 alternatively for one clock
cycle.
Application:
1. Counters.
2. Frequency Dividers.
3. Register.
39

40. T - Flip Flop (TOGGLE)
40

41. 41

42. Working for T – Flip Flop :
* The T - flip flop is also known as the
TOGGLE - flip flop. The toggle mode of JK flip
flop is used as T - Flip flop.
* This Flip flop can be obtained from a JK
flip flop when inputs J and K are connected to
provide a single input designated by T.
* The T flip-flop is a single input version of
the JK flip - flop. The T flip flop is obtained from
the JK type if both inputs are tied together.
42

43. * The output of the T flip-flop "toggles" with
each clock pulse.
* When t=0, (j=0, k=0) the clock transition
does not change.
* When t=1, (j=1, k=1) the clock transition
complements the state.
43

44. Sequential Circuit
* Sequential Logic circuits remember
past inputs and past circuit state.
* Outputs from the system are “fed
back” as new inputs
With gate delay and wire delay
* The storage elements are circuits
that are capable of storing binary
information: memory
44

45. Sequential Circuits :
45
Sequential Circuits Diagram
Circuits that we
have learned
so far
Information Storing
Circuits
Timed “States”

46. 46
Synchronous Sequential Circuits:
Flip flops as state memory
The flip-flops receive their inputs from theThe flip-flops receive their inputs from the
combinational circuit and also from a clock signalcombinational circuit and also from a clock signal
with pulses that occur at fixed intervals of time, aswith pulses that occur at fixed intervals of time, as
shown in the timing diagram.shown in the timing diagram.

47. Thank You
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