LogicGates
Question 1 
Consider the Boolean function z(a,b,c).
Which one of the following minterm lists represents the circuit given above?
Which one of the following minterm lists represents the circuit given above?
Z=Σ(0,1,3,7)
 
Z=Σ(2,4,5,6,7)
 
Z=Σ(1,4,5,6,7)  
Z=Σ(2,3,5)

Question 1 Explanation:
The output of the given circuit is a+b’c.
Convert a+b’c into canonical form which is sum of minterms.
a+b’c = a(b+b’)(c+c’)+ (a+a’)b’c
= abc + abc’ + ab’c + ab’c’ + ab’c + a’b’c
=Σ(7,6,5,4,1)
Convert a+b’c into canonical form which is sum of minterms.
a+b’c = a(b+b’)(c+c’)+ (a+a’)b’c
= abc + abc’ + ab’c + ab’c’ + ab’c + a’b’c
=Σ(7,6,5,4,1)
Question 2 
Let ⊕ and ⊙ denote the Exclusive OR and Exclusive NOR operations, respectively. Which one of the following is NOT CORRECT?
Question 2 Explanation:
Question 3 
Which one of the following circuits is NOT equivalent to a 2input XNOR (exclusive NOR) gate?
Question 3 Explanation:
All options except option ‘D’ gives EXNOR gates
Question 4 
What is the Boolean expression for the output f of the combinational logic circuit of NOR gates given below?
Question 4 Explanation:
f = ((P’Q’ + Q’R’)’ + ( P’R’ + Q’R’)’ )’
= (P’Q’ + Q’R’)( P’R’ + Q’R’)
= (P’Q’P’R’ + P’Q’Q’R’ + Q’R’P’R’ + Q’R’Q’R’)
= (P’Q’R’ + P’Q’R’ + P’Q’R’ + Q’R’)
= (P’Q’R’ + Q’R’)
= (Q’R’)
= (Q+R)’
= (P’Q’ + Q’R’)( P’R’ + Q’R’)
= (P’Q’P’R’ + P’Q’Q’R’ + Q’R’P’R’ + Q’R’Q’R’)
= (P’Q’R’ + P’Q’R’ + P’Q’R’ + Q’R’)
= (P’Q’R’ + Q’R’)
= (Q’R’)
= (Q+R)’
Question 5 
What is the minimum number of gates required to implement the Boolean function (AB+C) if we have to use only 2input NOR gates?
2  
3  
4  
5 
Question 5 Explanation:
NOR is Complement of OR
AB+C
= (A+C)(B+C) ← Distribution of + over
= ((A+C)’+(B+C)’)’
1st NOR (A+C)’. Let X = (A+C)’
2nd NOR (B+C)’. Let Y = (B+C)’
3rd NOR (X+Y)’
AB+C
= (A+C)(B+C) ← Distribution of + over
= ((A+C)’+(B+C)’)’
1st NOR (A+C)’. Let X = (A+C)’
2nd NOR (B+C)’. Let Y = (B+C)’
3rd NOR (X+Y)’
Question 6 
What is the minimum number of NAND gates required to implement a 2input EXCLUSIVEOR function without using any other logic gate?
3  
4  
5  
6 
Question 6 Explanation:
To create 2input ExclusiveOR function we require 4 NAND gates.
Question 7 
Consider the following circuit composed of XOR gates and noninverting buffers.
The noninverting buffers have delays d1 = 2 ns and d2 = 4 ns as shown in the figure. Both XOR gates and all wires have zero delay. Assume that all gate inputs, outputs and wires are stable at logic level 0 at time 0. If the following waveform is applied at input A, how many transition(s) (change of logic levels) occur(s) at B during the interval from 0 to 10 ns ?
1  
2  
3  
4 
Question 7 Explanation:
⇒ a will always be equal to A.
Question 8 
x NAND X  
x NOR x  
x NAND 1  
x NOR 1 
Question 8 Explanation:
Question 9 
A = 0, B = 0, C = 1  
A = 0, B = 1, C = 1  
A = 1, B = 0, C = 1  
A = 1, B = 1, C = 1 
Question 9 Explanation:
So the above equation is satisfied if either C=0 or A=0 and B=1.
Hence, Option (B) is correct.
Question 10 
Which of the following operations is commutative but not associative?
AND  
OR  
NAND  
EXOR 
Question 10 Explanation:
NAND operation is commutative but not associative.
Question 12 
exclusive OR  
exclusive NOR  
NAND  
NOR  
None of the above 
Question 12 Explanation:
So finally, we can write
There are 12 questions to complete.