Logic Gates : MCQs & PYQs with Explanation

Option A

A NOR gate is the complement of the OR gate. It gives output 1 only when all inputs are 0.
Boolean Expression : = (A+B)′
An XOR gate gives output 1 when the inputs are different or if the number of 1’s are odd and 0 when the inputs are the same.
Boolean Expression : = A⊕B
Now the given expression is (NOR)OR(XOR) i.e., (A+B)’ + (A⊕B)

Now, we construct the truth tables of NAND, OR, and AND gates and verify their behavior using the given equation.

The NAND gate behavior exactly matches with given expression.
Therefore, (NOR)OR(XOR) = NAND

Option B

A NAND gate produces the output as the negation of the AND operation, i.e., Y=(A⋅B)’. If one of its inputs is permanently connected to 0, then the AND operation becomes 0⋅B=0. So, Y=(0⋅B)′=0′=1. This means the output of the NAND gate will always be 1 regardless of the other input. Hence, the correct answer is 1.

Option B

The X-NOR gate, produces a high (1) output when both inputs are the same, either both 0 or both 1.
Truth—Table:

Option B

Given Boolean expression:
=AB+AB’C+AB’C’
=AB+AB’(C+C’)
=AB+AB’.1
=AB+AB’
=A(B+B’)
=A.1
=A

The given expression simplifies to A, so the output can be directly taken from input A. Therefore, the minimum number of NAND gates required is zero.

Option D

The EX-NOR (Exclusive-NOR) gate is the complement of the EX-OR (Exclusive-OR) gate. While an EX-OR gate gives output 1 when the inputs are different, the EX-NOR gate gives output 1 when the inputs are the same that means, both inputs are 0 or both are 1.

The Boolean expression for an EX-NOR gate is:
Y=A⊙B = (A⊕B)’ =  A.B+A’B’

Option B

The XOR (Exclusive OR) is a logical operation that compares two bits and gives the result 1 only when the inputs are different, and 0 when the inputs are the same.
The XOR operation has an important property, when a number is XORed with itself, the result is always 0, i.e., A ⊕ A = 0.
Given: A = 10101010. Now perform XOR with itself:   10101010 ⊕ 10101010 =  00000000

Option D

Digital electronics are devices that operate using binary signals. They process information in discrete steps rather than continuous signals.
Examples of digital electronic devices include computers, which use digital circuits for all processing tasks, mobile phones, which contain digital processors and memory and digital cameras, which convert images into digital data.

Option B

An X-NOR gate is a digital logic gate that gives output 1 when both inputs are the same (either both 0 or both 1), and gives output 0 when the inputs are different. 
It is also called an Equivalence Gate because it checks whether two inputs are equal.

Option D

A truth table is used in digital electronics to show all possible combinations of input variables and their corresponding outputs.
Each variable in a truth table can have only two possible values either 0 or 1. If there are n variables, then each variable contributes 2 possible combinations. Therefore, total possible combinations (rows) become 2ⁿ.

Option A

An Exclusive-OR (XOR) gate gives output 1 only when the two input bits are different. If both inputs are same, the output becomes 0.
The Boolean expression of XOR gate is A’B+AB’. Here option (A) uses different variable names (C and D) but represents the same XOR expression: C’D+CD’