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Binary Subtraction

Half Subtractor - Truth Table, Boolean Expression & Logic Circuit | Logicroo

Learn the Half Subtractor with interactive circuit diagrams, truth tables, Boolean expressions, difference and borrow logic, logic gate implementation, and digital logic examples.

Half Subtractor

Binary Subtraction

A half subtractor takes two single bits, A (minuend) and B (subtrahend), and computes their difference. Diff = A ⊕ B tells you the result bit; Borrow = A′ · B tells you whether the subtraction needed to borrow from the next higher bit (only happens when A = 0 and B = 1).

Inputs
Diff
0
Borrow
0
A − B
0 − 0
Delay
Diff = A ⊕ B (1 gate delay, XOR)
Borrow = A′ · B (2 gate delay, NOT then AND)
Borrow is set only when A = 0 and B = 1, i.e. B is being taken from a bit that has nothing to give.
Truth table
ABDiffBorrow