Introduction:
The exclusive OR (XOR) gate is essential in parity generation, adders, and control logic. Understanding when its output goes HIGH is fundamental for designing and analyzing digital circuits.
Given Data / Assumptions:
- 2 inputs: A and B
- Binary levels only (0 and 1)
- Ideal logic with no undefined states in normal operation
Concept / Approach:
XOR outputs 1 if and only if exactly one input is 1. In other words, the inputs must differ. If both inputs are equal (00 or 11), XOR outputs 0.
Step-by-Step Solution:
Step 1: Write XOR condition: X = 1 when A != B.Step 2: Evaluate pairs: 00 → 0, 01 → 1, 10 → 1, 11 → 0.Step 3: Conclude output is HIGH only for unequal inputs (01 and 10).
Verification / Alternative check:
Truth table enumeration or algebraic identity: A XOR B = A NOT B + NOT A B; both terms cannot be true at the same time when inputs are equal.
Why Other Options Are Wrong:
Both inputs are 0: Produces 0 for XOR.Both inputs are 1: Produces 0 for XOR.Both inputs are undefined: Standard XOR truth table does not rely on undefined states.
Common Pitfalls:
Confusing XOR with OR; OR is high for 01, 10, and 11.Assuming equality creates a high output; that is XNOR, not XOR.
Final Answer:
Inputs are unequal
Discussion & Comments