Identify “one-or-the-other” logic Which logic circuit outputs HIGH if one input or the other input, but not both, is HIGH?

Introduction / Context:Sometimes we require a signal that indicates exclusivity: exactly one of two conditions is true. The exclusive-OR (XOR) gate implements this function at the 1-bit level and is widely used in arithmetic and parity generation.

Given Data / Assumptions:

• Two inputs A and B.
• Desired behavior: X = 1 when A ≠ B; X = 0 when A = B.

Concept / Approach:The XOR truth table is 1 for input pairs 01 and 10, and 0 for 00 and 11. This matches “one or the other, but not both.”

Step-by-Step Solution:

Verification / Alternative check:Boolean identity: X = A XOR B = (A + B) * (NOT(A*B)). It is OR gated with the complement of AND, ensuring not both.

Why Other Options Are Wrong:

• Ex-NOR: True for equality (both same), opposite of exclusivity.
• OR: True for 11 as well, violating “not both.”
• NAND: False only when both are 1; not the exclusive function.

Common Pitfalls:Assuming OR implies exclusivity; OR includes the both-true case, whereas XOR excludes it.

Final Answer:Ex-OR gate