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Half-adder capability check in digital arithmetic: Which functional element is not provided by a standard half-adder circuit when adding two single-bit operands?

Difficulty: Easy

Correct Answer: carry in

Explanation:


Introduction / Context:
Adders are fundamental combinational blocks for arithmetic units in CPUs, DSPs, and ALUs. The two basic building blocks are the half-adder and the full-adder. Knowing the exact capabilities and limitations of each helps you choose the appropriate component when chaining bits into multi-bit adders or designing fast adder architectures.

Given Data / Assumptions:

  • A half-adder has two primary data inputs (A and B).
  • Outputs are SUM and CARRY-OUT.
  • No prior carry-in is assumed for a half-adder stage.


Concept / Approach:
A half-adder computes SUM = A XOR B and CARRY-OUT = A * B. It is “half” because it does not accept a carry-in from a less significant stage. In contrast, a full-adder has three inputs (A, B, and CARRY-IN) and two outputs (SUM and CARRY-OUT), enabling cascading across bit positions in multi-bit addition.

Step-by-Step Solution:

List half-adder I/O: inputs = A, B; outputs = SUM, COUT.Check for carry-in: not present in the half-adder definition.Identify the missing capability: lack of CARRY-IN support.Therefore, the half-adder does not have a carry-in input.


Verification / Alternative check:

Compare with full-adder equations: SUM = A XOR B XOR CIN; COUT = A*B + (A XOR B)*CIN. The extra input CIN is the distinguishing feature.


Why Other Options Are Wrong:

carry out: A half-adder does produce a carry-out (A*B).two inputs: It has exactly two inputs by definition.all of the above: Incorrect because only carry-in is missing.


Common Pitfalls:

Assuming a half-adder can be dropped into any bit position of a ripple adder; without CIN it cannot handle propagation from lower bits.Confusing half-adder (2 inputs) with full-adder (3 inputs).


Final Answer:

carry in
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