A half subtractor computes A minus B and produces a difference and borrow. A full subtractor also includes an incoming borrow. Borrow indicates that the current bit position needed one unit from the next higher position to complete its subtraction.
Worked example
For a half subtractor, A = 0 and B = 1 gives difference = 1 and borrow = 1: borrowing makes the local subtraction 2 − 1. For a full subtractor with A = 0, B = 1 and Bin = 1, the local total is −2, giving difference = 0 and borrow-out = 1.
What to watch for
Borrow and carry are different conventions. If subtraction is implemented with an adder, the final carry often means no borrow; check the chosen interface definition.
Try it yourself
What are the half-subtractor outputs for A = 1 and B = 0?
Answer: Difference = 1 and borrow = 0. No higher-position contribution is needed.
How to study this topic
State the operand width and signedness first. Work out a decimal answer, then compare it with the binary result. Keep result bits, carry, borrow and signed overflow distinct when interpreting the circuit's output.
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Digital Electronics