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In: Computer Science

2)Prove, using Boolean Algebra theorems, that the complement of XOR gate is XNOR gate (Hint :...

2)Prove, using Boolean Algebra theorems, that the complement of XOR gate is XNOR gate (Hint : Prove that AB + AB = AB + AB by using De-Morgan’s theorem)

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Expert Solution

ANSWER:

THE FOLLOWING IMAGE SHOWS THE PROOF THAT COMPLEMENT OF BOOLEAN ALGEBRAIC EXPRESSION OF XOR IS XNOR

To understand it better here is the truth table of XOR gate and complementing the output of it to show the truth table of XNOR gate.

XOR GATE TRUTH TABLE:

A B Y(OUTPUT)
0 0 0
0 1 1
1 0 1
1 1 0

COMPLEMENTING XOR GATE TRUTH TABLE TO GET XNOR GATE OUTPUT:

A B Y
(XOR)

Y COMPLEMENT
(XNOR)
0 0 0 1
0 1 1 0
1 0 1 0
1 1 0 1

SUMMARY:

The image shows the proof that complement of XOR gate is XNOR gate using DeMorgan's Law which are also stated in there. Along with it, the truth table is provided to understand the output when 0/1 is given as values to the Boolean Expression.

Note: If you have any queries than let me know in the comments. If you find it helpful than a Like would be appreciated.

venereology answered 1 year ago
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