Question

A two input XOR Gate produces a high output only when its both inputs are:
(A) same
(B) different
(C) low
(D) high

Answer 1

Hint: The XOR gate stands for an Exclusive-OR gate. An Exclusive-OR gate is a kind of digital logic gate which gives a true output when the number of true inputs is odd. We shall use its Boolean expression and truth table diagram to determine the outputs of an XOR gate, and thus concluding when exactly can an XOR gate produce a high input.

Complete step-by-step solution:
Let us assume that the two inputs of our XOR gate is denoted by A and B. And, the resultant of these two inputs is denoted by Q. Then, this resultant can be expressed as a Boolean expression in terms of our inputs A and B.
The Boolean expression for XOR gate is given as follows:
$\Rightarrow X=A.\overline{B}+\overline{A}.B$
This could also be written as:
$\Rightarrow X=(A+B).(\overline{A}+\overline{B})$
Simplifying the above Boolean expression, we get:
$\Rightarrow X=A\oplus B$
Now, we will see the different cases for the above Boolean expression.
Case (1): If, $A=0,B=0$ ,then:
$\Rightarrow X=0$
Case (2): If, $A=0,B=1$ ,then:
$\Rightarrow X=1$
Case (3): If, $A=1,B=0$ ,then:
$\Rightarrow X=1$
Case (4): If, $A=1,B=1$ ,then:
$\Rightarrow X=0$
Now, we can construct the truth table for an XOR gate as follows:

Input (A)	Input (B)	Output (X)
0	0	0
0	1	1
1	0	1
1	1	0

Hence, from the above Truth Table of an XOR gate, we can conclude that, a two input XOR Gate produces a high output only when both the inputs are different.
Hence, option (B) is the correct option.

Note: For a two input XOR gate, the resultant expression could be remembered as, “in order to get a true output, we must have one or the other but not both at the same time”. Apart from being used as a 2-half bit adder. These XOR gates are used in making Clocks, Buffer and inverters too.