The document contains a comprehensive analysis of number system conversions (octal, hexadecimal, and binary) including step-by-step calculations. It explains various digital logic components like OR and NAND gates, encoders, and decoders with their respective truth tables and functional definitions. Additionally, it discusses the utility of logic probes in troubleshooting digital circuits.

1. Prepared by:
Abdul Quddus
Class:
BSCS 2nd (regular)
Roll no:
BCSF19BM039
Course:
Digital Logic Design
Instructor:
Mr.Kamran Shah

2. Question no: 1
Conversion:
(A) Octal 623.77 to Decimal, Binary and Hexadecimal
1. Octal to decimal:
Solution:
623.778 = 6∙82+2∙81 +3∙80 +7∙8-1 +7∙8-2
=384+16+3+0.875+0.109375
= 403.98437510
Happened: 403.9843710

3. 2. Octal to Binary:
Solution:
Converting 403.98437510 in
Binary system here
Whole part of a number is
obtained by dividing on the basis new
40310 =1100100112

4. 0
.
984375
2
1 96875
2
1 9375
2
1 875
2
1 75
2
1 5
2
1 0
623.778 = 110010011.1111112
The fractional part of number is found by
multiplying on the basis new:
0.98437510 = 0.1111112
Add up together both parts here so:
1100100112 + 0.1111112 =
110010011.1111112
Result of converting:

5. 3. Octal to Hexadecimal:
Solution:
Converting 403.98437510 in Hexadecimal system here
so:
Whole part of a number is obtained by dividing on the
basis new
Happened:
40310 = 19316

6. The fractional part of number is found by multiplying on
the basis new
Happened:
0.98437510 = 0.FC16
Add up together whole and fractional
part here so:
19316 + 0.FC16 = 193.FC16
Result of converting:
623.778 = 193.FC16

7. (b) Hexadecimal 2AC5.D to Decimal, Octal, and Binary.
1. Hexadecimal to decimal:
Solution:
Translate it to decimal here:
2AC5.D16 = 2∙163 +10∙162 +12∙161 +5∙160 +13∙16-1
=8192+2560+192+5+0.81
= 10949.812510
Result :
2AC5.D16 = 10949.812510

8. 2. Hexadecimal to Octal:
Solution:
Result of converting in t decimal :
2AC5.D16 = 10949.812510
Converting 10949.812510 in octal system
here so:
1094910 =253058

9. The fractional part of number is found by multiplying
on the basis new
0.812510 = 0.6488
Add up together whole and fractional part here so:
253058 + 0.648 = 25305.648
Result after converting:
2AC5.D16 = 25305.648

10. 3.Hexadecimal to Binary:
Solution:
Converting 10949.812510 in Binary
System here so:
Whole part of a number is obtained by
dividing on the basis new
1094910 = 101010110001012

11. The fractional part of number is found by multiplying
on the basis
Happened:
0.812510 = 0.11012
Add up together whole and fractional part here
so:
= 101010110001012 + 0.11012
= 10101011000101.11012
Result of converting:
2AC5.D16 = 10101011000101.11012

12. Question no: 2
(a) OR Gate:
• An OR gate has two or more than two inputs
and one output signal.
• It is called an OR gate because the output signal
will be high only if any or all input signals are
high.
• The OR gate follow the logical operation of the
input and output signals. It permits the signal to
pass and stop through it.

13. Logic Symbol:
The logic symbol for the gate is shown below.

14. Switching Circuit:
The switching circuit of the gate operation is shown below.

15. Explanation:
A lamp L is connected to a voltage source. A and B
are the two switches. The switching circuit
illustrates that the lamp L will glow when either of
the switches A or B or both A and B is closed. The
lamp will go off when both the switches are in the
open condition.

16. Truth Table:

17. (B) NAND Gate:
 The NAND gate is a combination of an AND gate
and NOT gate.
 They are connected in cascade form.
 It is also called Negated And gate.
 The NAND gate provides the false or low output
only when their outputs are high or true.
 The NAND gate is essential because different types
of a Boolean function are implemented by using it.

18. Functional Completeness:
The NAND gate has the property of functional
completeness. The function completeness means
any types of gates can be implemented by using the
NAND gate. It performs the function of OR, NOR
and AND gate.

19. Logic Symbol:
Logic Circuit:
From the logic circuit, the output can be expressed as:
Z=A.B

20. Switching Circuit:

21. Truth Table:
The truth table of the NAND gate is given below.
It is clear that all the input is kept high to
get low output

22. Question no: 3
Octal to Binary Encoder:
• An octal to binary encoder consists of eight
input lines and three output lines. Each input
line corresponds to each octal digit and three
outputs generate corresponding binary code.
• In encoders, it is to be assumed that only one
input is active or has a value 1 at any given time
otherwise the circuit has no meaning.

23. Logic Symbol:
The figure below shows the logic symbol of octal
to binary encoder.

24. Figure:
We can implement the octal to
binary encoder using set of OR
gates as shown in figure below.

25. Truth Table

26. Question no: 4
BCD to Decimal Decoder
Decoder:
o A decoder is a Combinational Circuit that
converts encoded signals back to its original form.
o The decoder circuit performs the exact opposite
function of an encoder.
o It accepts coded signals from the encoder and
generates the desired output.
o It is possible to operate a demultiplexer as a decoder.

27. BCD to Decimal Decoder:
This device is formed by a circuit that converts
Binary-Coded- Decimal into a 1-of-10 output.
Circuit Diagram:
The circuit diagram of BCD to the decimal decoder
is nothing but the demultiplexer circuit shown in
the below diagram.

28. Truth Table:

29. Question No#05
Draw a combinational logic circuit, define its all
parts and complete process with the help of
diagram?

30. LOGIC PROBE
What is logic probe:
• Logic probes are very cheap and easy to use as
simple digital testers in many applications. Logic
probes can provide a simple way of testing slow
moving digital logic levels and signals.
• It detects Logic Levels, which are discrete voltage
levels that represent 1’s and 0’s in a binary circuit.
• It indicates if a 1 or a 0 is present in a circuit.

31. What is logic probe
• This allows a designer to quickly troubleshoot a
circuit to see if Logic levels are being set correctly.
• They are usually found as small/handheld devices
that can be connected to any point in a circuit.
• They commonly light up an LED light that
indicates what the Logic Level is.

32. Figure

33. How Logic Probes Work
• Models like the one in Figure above are low-cost
because they are electrically quite simple, because
their job is simple: they’re designed to give a visual
and (usually) aural cue about the logic state of a
particular circuit line.
• One LED (light-emitting diode) on the probe lights
up if the logic is 0 (also referred to as LOW). See
Figure below.
• Another LED lights up if the logic is 1 (or HIGH).

34. How Logic Probe Work
• A third LED indicates a pulsing signal, one that rapidly
alternates between 0 and 1.
• A good logic probe can detect a logic gate pulsing at
speeds of up to 10 MHz (10 megahertz, or 10,000,000
times per second), which is more than fast enough for
most robotics applications, even when using computer
control.
• To use the logic probe you really have to know what
points in the circuit to test. This means you need to have
a schematic or other wiring diagram, so you know what
goes to where.

36. Logic Probe Circuit
RED
LED
GREEN

37. • +V and Ground are connected to the power of the
circuit to be probed (alligator clips).
• Probe can be a simple wire.
• The internal circuit runs from a 5V power supply
but an on-board regulator is provided, so the circuit
can be powered from a wide range of power
supplies.

38. Circuit on Breadboard

39. Using a Logic Probe
• Be careful when working close to any kind of high
voltage or current.
• Logic probes aren’t meant for testing these kinds of
circuits anyway, so if high voltage or current is
exposed in your circuit, cover that portion up so
you don’t actually touch it with your fingers or the
logic probe.
• It’s nearly impossible to blindly use the logic
probe on a circuit without knowing what you are
testing.