A full adder differs from a half adder in that it accepts a carry-in (C_in) in addition to the two operand bits, enabling multi-bit ripple addition. Evaluate this statement.

Introduction / Context:Adders are fundamental to digital systems. The distinction between half adder and full adder explains how wide adders are constructed from bit-slices and why carry chaining is possible.

Given Data / Assumptions:

• Half adder: inputs A, B → outputs SUM, C_out; no C_in.
• Full adder: inputs A, B, C_in → outputs SUM, C_out.
• Goal: enable multi-bit addition by propagating carry.

Concept / Approach:Because a full adder accepts a carry-in, it can be cascaded so that each bit position accounts for carry from the previous less significant bit. This is essential for correct multi-bit arithmetic and underlies ripple-carry and faster adder architectures.

Step-by-Step Solution:1) For LSB, set C_in = 0 (or external carry-in).2) Compute SUM and C_out at each bit with a full adder.3) Feed C_out(i) to C_in(i+1) to chain the bits.4) Obtain an N-bit sum with proper carry propagation.

Verification / Alternative check:Truth tables and standard FA implementations show explicit C_in handling; half adders lack this input.

Why Other Options Are Wrong:“Incorrect” denies the defining property. “Only half adders have carry-in” is backwards. “Full adders output only carry” omits the SUM output which is essential.

Common Pitfalls:Confusing half and full adder roles; not initializing the least significant carry-in properly.

Final Answer:Correct