In basic digital design, what logic function is produced at the SUM output of a half-adder circuit?

Introduction / Context:
The half-adder is one of the first combinational circuits studied in digital logic. It adds two single binary digits and produces a SUM bit and a CARRY bit. Knowing which Boolean function corresponds to the SUM output is essential for understanding adders and arithmetic logic units (ALUs).

Given Data / Assumptions:

• Inputs: A and B, each a single bit.
• Outputs: SUM and CARRY.
• No carry-in is present in a half-adder (unlike a full adder).

Concept / Approach:
The SUM output of a half-adder is 1 when exactly one of the inputs is 1. This is precisely the truth table of the Exclusive-OR function. The CARRY output is 1 only when both inputs are 1, which corresponds to the AND function.

Step-by-Step Solution:
1) Write the truth table for A, B → SUM:A=0, B=0 → SUM=0A=0, B=1 → SUM=1A=1, B=0 → SUM=1A=1, B=1 → SUM=02) Compare with standard logic functions.3) The pattern matches Exclusive-OR (XOR): SUM = A ⊕ B.

Verification / Alternative check:
Boolean expression: SUM = A*B' + A'B, which is the canonical XOR identity. The carry is CARRY = AB. Together, they implement binary addition for 1-bit inputs without carry-in.

Why Other Options Are Wrong:
AND: that is the CARRY output, not the SUM.XNOR: high when inputs are equal, which would give 1 at A=0,B=0 and A=1,B=1—opposite of SUM.NAND/OR: do not match the SUM truth table.

Common Pitfalls:
Confusing SUM with CARRY, or assuming SUM is a simple OR. Remember, SUM must be 0 when both inputs are 1 (since 1+1=10 in binary), hence XOR, not OR.

Final Answer:
Exclusive-OR (XOR)