How is the Ex-NOR gate related to Ex-OR, and what is its expression?

It is the complement of XOR: Y = AB + A'B'

It is the same as XOR: Y = AB' + A'B

It is the complement of AND: Y = A' + B'

It is the dual of OR: Y = A + B

Which application matches the XOR gate (sum output) and XNOR gate respectively?

Half adder sum; equality comparator

Equality comparator; half adder sum

2081 Chaitra (new course) · 3 marks

Short note: Ex-OR and Ex-NOR gate

Short answer

Ex-OR (XOR) outputs 1 when inputs differ (A≠B), given by A⊕B = A B' + A' B. Ex-NOR (XNOR) is its complement, outputting 1 when inputs are equal (A=B), used in comparators. XOR is used in half adders, parity generators.

Write a short note on Ex-OR and Ex-NOR gate.

Ex-OR (XOR) gate. It gives output 1 when its two inputs are different (odd number of 1s), and 0 when they are equal.

Y=A\oplus B=A\bar B+\bar AB

Ex-NOR (XNOR) gate. It is the complement of XOR. Output is 1 when the inputs are equal.

Y=\overline{A\oplus B}=AB+\bar A\bar B

A	B	XOR	XNOR
0	0	0	1
0	1	1	0
1	0	1	0
1	1	0	1

 A --|=\\
     |  )>-- A xor B        XNOR: same, with a bubble
 B --|=//                     (small circle) at the output

Applications:

XOR: half adder (sum $=A\oplus B$ ), binary adders/subtractors, parity generators and checkers, controlled inverter, binary-to-Gray code conversion.
XNOR: equality (comparator) circuits, which give 1 when two bits are the same.

✓ Answer checked by Claude Opus 5.5 (high effort)

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Short note: Ex-OR and Ex-NOR gate

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