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Binary Subtraction

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

Learn the Full Subtractor with interactive circuit diagrams, truth tables, Boolean expressions, Difference and Borrow logic, logic gate implementation, and digital logic examples.

Full Subtractor

Binary Subtraction

A full subtractor extends the half subtractor with a borrow-in (Bin) from the previous stage, so bits can be chained to subtract multi-bit numbers. Diff = A ⊕ B ⊕ Bin. Bout is set whenever a borrow is needed either from the A/B stage or from the Bin stage: Bout = (A′·B) + (A′·Bin) + (B·Bin). It's built from two half subtractors and an OR gate, the same way a full adder is built from two half adders.

Inputs
Diff
0
Bout
0
A − B − Bin
0 − 0 − 0
Delay
D1 = A ⊕ B, Bo1 = A′·B (half subtractor 1)
Diff = D1 ⊕ Bin, Bo2 = D1′·Bin (half subtractor 2)
Bout = Bo1 + Bo2 (1 gate delay, OR)
Bout is set if the A/B stage needed a borrow, or the Bin stage needed one.
Truth table
ABBinDiffBout