Lab4 for TOA

1. Federal Urdu university of
arts science and technology
Assignment no. 4
Name: Zamin Shakeel (Repeater)
Class: BSCS 2D
Subject: Digital Logic Design (LAB)
Teacher: Sir Imran

2. Task # 4.1:
 Simplify the following function
F=A’D + BD + B’C + AB’D
= B D + B’ C + D (A B’ + A’)
= B D + B’ C + D (B’ + A’)
= B D + B’ C + D B’ + D A’
= D (B + B’) + B’ C+ D A’
= D 1 + B’ C+D A’
= D + B’ C+ D A’
F=B’C + D
 Obtain the truth table
 Simulate the circuit in Proteus and build it on bread board.
 Mention the total number of gates used to implement the original function and the
simplified one.
Circuit:

3. Truth Table:
B C D F
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 0
1 1 1 1
Conclusion:
The gates are reduced after simplification.
Without Simplification: F=A’D + BD + B’C + AB’D
AND=4
NOT=2
OR= 1
With Simplification: F=B’C + D
AND=1
NOT=1
OR= 1
Task # 4.2:
 Simplify the function F1.
F= A’. B’.C’+A’. B’.C+A’.C’
= A’ B’ C + A’ C’
= A’ (B’ C + C’)
= A’ (B’ + C’)
F=A’ B’ + A’ C’
 Obtain the simplified SOP expression and the truth table.
 Simulate the circuit and build it on bread board.

4. Circuit:
Truth Table:
A B C F
0 0 0 1
0 0 1 1
0 1 0 1
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 0
Conclusion:
The gates are reduced after simplification.

5. Task # 4.3:
 Derive the function from the given circuit, simplify it and implement the simplified
circuit.
 Mention the total number of gates used to implement the original function and the
simplified one.
F=ABC + A’C + BC’D + AB’C
= C (A B + A’) +B C’ D +A B’ C
= C (B+ A’) +B C’ D+A B’ C
= C B+C A’ +B C’ D+A B’ C
= C A’ +B (C’ D+C) +A B’ C
= C A’ +B (D+C) +A B’ C
= B (D+C) +C (A B’ + A’)
= B (D+C) +C (B’ + A’)
= B D+B C+C (B’ + A’)
= B D+B C+C B’ +C A’
= B D+C (B + B’) +C A’
= B D+ C + C A’
F=BD + C

6. Simplified Circuit:
Truth Table:
b c d X
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1

7. Conclusion:
The gates are reduced after simplification.
Without Simplification: F=ABC + A’C + BC’D + AB’C
AND=4
NOT=3
OR= 1
With Simplification: F=BD + C
AND=1
NOT=0
OR= 1
Answer the following questions
1. How does minimization help in reducing the circuit’s complexity?
Ans: Minimization helps in reducing complexity of circuit by decreasing the inputs and
gates in that circuit. lesser the gates and variables lesser the complexity is
2. For the function F= A’B’D+A’BD+AC’D+ACD+AB’D’
a) Simulate the circuit without simplification
F = A’B’D+A’BD+AC’D+ACD+AB’D’

8. b) Simulate the circuit with simplification
F = A’B’D+A’BD+AC’D+ACD+AB’D’
= A’ D (B’ + B) +A C’ D+A C D+A B’ D’
= A’ D 1 +A C’ D+A C D+A B’ D’
= A’ D +A C’ D+A C D+A B’ D’
= D (A C’ + A’) +A C D+A B’ D’
= D (C’ + A’) +A C D + A B’ D’
= D C’ +D A’ + A C D+ A B’ D’
= D A’ +D (A C+ C’) + A B’ D’
= D A’ +D (A+ C’) + A B’ D’
= D A’ +D A+D C’ + A B’ D’
= D (A’ + A) +D C’ +A B’ D’
= D 1 +D C’ +A B’ D’
= D + D C’ +A B’ D’
= D + A B’D’
F = AB’+D