Using XOR as a controlled inverter Show from the truth table how an exclusive-OR (XOR) gate can invert the data on one input when the other input acts as a control.

Introduction / Context:
The XOR function is invaluable for conditional inversion. Treating one input as a control line turns XOR into a 1-bit multiplexer between “pass-through” and “invert” behaviors, used in arithmetic units and data encoding.

Given Data / Assumptions:

• XOR definition: X = A XOR B = 1 when inputs differ, 0 when equal.
• Let A be the control input; B is the data input.
• We want X to equal B when A = 0, and X to equal NOT B when A = 1.

Concept / Approach:
From the XOR truth table: X = A XOR B = (NOT A AND B) OR (A AND NOT B). This directly encodes pass-through for A = 0 and inversion for A = 1.

Step-by-Step Solution:

Verification / Alternative check:
Algebraic rewrite: X = B XOR A = B when A = 0; X = NOT B when A = 1. Hardware implementations of adders use this to conditionally complement operands.

Why Other Options Are Wrong:

• Same as B for both A values: Ignores XOR behavior; that would be a buffer.
• Inverse when A = 0 and same when A = 1: Reversed from XOR’s property.
• Inverse for both A values: That would be a pure inverter, not controlled.

Common Pitfalls:
Swapping the role of control and data, or confusing XOR with XNOR (which is equality, not inversion control).

Final Answer:
Using A as the control, when A = 0, X is the same as B. When A = 1, X is the inverse of B.