Logic Gates Questions and Answers

Answer: B

The NAND expression is (A·B)'.

NAND is NOT-AND: the output is the complement of A AND B, so it is 0 only when both inputs are 1.

(A + B)' is NOR, A + B is OR, and A·B is AND. NAND and NOR are called universal gates because any logic circuit can be built from either alone.

Truth table check for NAND: inputs 00, 01 and 10 give 1, and only 11 gives 0, which is exactly the complement of AND.

Answer: C

In OR gate  we need atleast one bit to be equal to 1 to generate the output as 1 because OR means  any of the condition out of two is equal to 1  which means  if atleast one input is 1 then it shows output as 1 . Number of 1's in input may be more than one but the output will always be 1 in OR gate. So the answer is 'C'.

Answer: C

Correct answer: Propagation time

Propagation delay is the interval between a change at a gate's input and the corresponding change at its output. Rise and decay times describe the shape of the transition itself rather than the lag between input and output.

Answer: A

Correct answer: Operating speed

The operating speed of a gate is the highest frequency at which it can still follow its input - set by its propagation delay, since a gate cannot respond faster than it can switch.

Answer: C

Y=A+B. This is the equation of OR gate. We require 3 NAND gates to create  OR gate.  We can also write

After 1st NAND operation
Y = (A AND B)' 
Y=  A'  + B'  (Demorgan's Law)
After 2nd NAND operation
Y= ( A'  + B')'
Y=  A . B  (Demorgan's Law)
After 3rd  NAND operation
Y= ( A . B )'
Y=  A' +  B '  (Demorgan's Law)

So we need 3 NAND gates.

Answer: D

Correct answer: XOR gate

An XOR gate outputs 1 when an odd number of its inputs are 1, which is exactly what a parity test asks. Chaining XOR gates over a word therefore gives 1 for odd parity and 0 for even. AND, OR and NOR have no such property.

Answer: D

Correct answer: AND

The AND gate outputs 1 only for the single input combination in which every input is 1. NAND is its complement, giving 0 only in that case, while OR needs just one HIGH input.

Answer: D

Correct answer: Three bit parity checker

The sum output of a full adder is \( A \oplus B \oplus C_{in} \) - it is 1 whenever an odd number of the three inputs is 1. That is precisely what a three-bit parity checker computes. The carry output, by contrast, is the majority function of the same three bits.

Answer: B

Correct answer: 1 half-adder, 15 full-adders

The least significant bit has no carry coming into it, so a half adder suffices there; each of the remaining fifteen bits must add three quantities - two bits and a carry - which needs a full adder. In general an n-bit ripple adder takes one half adder and \( n-1 \) full adders.

Answer: B

Correct answer: Decay time

Decay time, or fall time, is measured between the 90 per cent and 10 per cent points on the falling edge, mirroring rise time on the leading edge. The 10 and 90 per cent marks are used because the extremes of the transition are hard to locate.