Question

For the XNOR gate truth table shown below, the values of \[w\], \[x\], \[y\], and \[z\]are _______, ________, _________ and ________, respectively.

A. 1, 0, 0, 1
B. 0, 1, 0, 1
C. 1, 1, 1, 0
D. 1, 0, 0, 0,

Answer 1

Hint: The XNOR gate is a digital logic gate whose function is the logical complement of the exclusive OR ( XOR ) gate. The algebraic notation to represent the XNOR operation is \[S = A \odot B\]. To find the outputs of XNOR gate we must know the basic concept XNOR gate.

Complete step by step solution:
As we all know that the output of XNOR gate is 1 ( also called as high value ) only when both of the inputs to the gate are the same ( whether it is 0 or 1 ) and if the inputs of the gate are different then the output is always 0. Let us understand with a diagram.

Now by keeping this concept of XNOR gate in mind we had to find the output of inputs that are given in the table above.
As first input values are 0 and 0 ( both are the same ) so the output must be 1.
So, output w = 1
Similarly, second and third inputs have different values so the output must be 0.
So, output x = y = 0
And the fourth inputs are the same so their output must be 1.
So, output z = 1.
So, the output values are
w = 1
x = 0
y = 0
z = 1
Hence A is the correct option.

Note: Whenever we had to find the values of output of any gate ( here XNOR ) then we must know the calculation or the conditions which had an impact on the output of that gate. The two input version implements logical equality behaving according to the truth table to the right, and hence the gate is sometimes called an “ equivalence gate “.