Introduction to CS

Project 5: Logic Gates - Answers

1. Create a Truth Table for the following circuit:

D = NOT (A OR B)
E = B * C
Q = D OR E = (NOT (A OR B)) OR (B * C)

Inputs Outputs
 A   B   C   D   E   Q 
0 0 0 1 0 1
0 0 1 1 0 1
0 1 0 0 0 0
0 1 1 0 1 1
1 0 0 0 0 0
1 0 1 0 0 0
1 1 0 0 0 0
1 1 1 0 1 1

 

2. Replace gates with NAND gates only - NAND Gate Synthesis

3. Eliminate redundancy in circuit

4. Create new Truth Table and verify output Q matches on both tables - Q1 from first circuit and Q2 from the new replacement NAND circuit - to "Prove" our results.

Inputs
Outputs
 A 
 B 
 C 
D
E
F
G
 Q1 
 Q2 
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
  • D = NOT A
  • E = NOT B
  • F = NOT(D * E)
  • G = NOT(B * C)
  • Q1 = NOT(F * G)