GATE Digital Logic 2 — Questions and Answers
Question 1: Which Boolean expression represents the output of an XNOR gate with inputs A and B?
- A⊕B
- A·B + A'·B' (Correct answer)
- A'+B'
- A·B'
Correct answer: A·B + A'·B'
XNOR outputs 1 when both inputs are equal, expressed as A·B + A'·B'.
Question 2: A 4-bit ripple carry adder adds two 4-bit numbers. What is the maximum number of gate delays for carry propagation?
- 4
- 8 (Correct answer)
- 6
- 2
Correct answer: 8
Each full adder introduces 2 gate delays for carry, so 4 stages yield 8 gate delays total.
Question 3: The minimum number of NAND gates required to implement the function F = A·B + C is:
- 3 (Correct answer)
- 4
- 2
- 5
Correct answer: 3
F = A·B + C can be realized with 3 NAND gates: NAND(A,B), NAND(C,C), and NAND of their outputs.
Question 4: In a JK flip-flop, what is the output when J=1, K=1 and a clock pulse is applied?
- Q=0, Q'=1
- Q=1, Q'=0
- Q toggles to complement (Correct answer)
- No change
Correct answer: Q toggles to complement
When J=K=1, the JK flip-flop toggles its output on each clock pulse.
Question 5: Which of the following is a universal gate?
- AND
- OR
- NAND (Correct answer)
- XOR
Correct answer: NAND
NAND (and NOR) are universal gates because any Boolean function can be implemented using only NAND gates.
Question 6: The decimal number 45 in BCD (Binary Coded Decimal) is represented as:
- 0100 0101 (Correct answer)
- 0010 1101
- 1010 1011
- 0100 1001
Correct answer: 0100 0101
BCD encodes each decimal digit separately: 4 = 0100, 5 = 0101, giving 0100 0101.
Question 7: A multiplexer with n select lines can have at most how many input lines?
- n
- 2n
- n²
- 2^n (Correct answer)
Correct answer: 2^n
An n-select-line multiplexer can select among 2^n inputs, one per select combination.
GATE Digital Logic 2
Which Boolean expression represents the output of an XNOR gate with inputs A and B?