Binary addition fact — evaluate the statement: “The addition 1 + 0 doesn’t generate a carry bit; one does not exist.” Consider one-bit addition rules and carry generation conditions.

Introduction / Context:
Binary addition follows simple truth rules for single bits with an optional carry-in. Understanding when a carry is generated is fundamental to adder design (half adders, full adders) and to analyzing arithmetic overflows. Here, we assess whether adding 1 and 0 alone generates a carry.

Given Data / Assumptions:

• One-bit addition without an incoming carry (carry-in = 0).
• Values being added: 1 and 0.
• We focus on carry generation in that minimal case.

Concept / Approach:
Binary single-bit addition tables state: 0+0 → sum 0, carry 0; 0+1 or 1+0 → sum 1, carry 0; 1+1 → sum 0, carry 1. Carries occur when the arithmetic sum is 2 or greater. The pair 1 and 0 sums to 1, which is below the threshold for carry generation.

Step-by-Step Solution:

Verification / Alternative check:
Truth tables for half adders confirm the result; full adder truth tables show the dependency on carry-in. Implementation in logic (XOR for sum, AND for carry in the 1+1 case) reflects the same rule.

Why Other Options Are Wrong:

• Incorrect: Conflicts with standard adder logic.
• “Only correct if previous carry-in is zero”: The statement already assumes no carry-in; with carry-in = 1, the situation changes, but that is a different scenario.
• “Only correct for signed addition”: Signedness affects interpretation of overflow, not single-bit carry rules.

Common Pitfalls:
Confusing carry with overflow; in signed arithmetic, overflow detection has separate rules and is not identical to carry-out in two’s complement.

Final Answer:
Correct — 1 + 0 (with no carry-in) yields sum 1 and no carry.