Full Subtractor
Subtracts B and Bin from A. Built from two XOR + two NOT + two AND + one OR gate. Difference = A ⊕ B ⊕ Bin · Borrow = (Ā·B) + (Ā·Bin) + (B·Bin)
Full Subtractor Circuit
DIFF = 0
BORROW = 0
Truth Table
| A | B | Bin | Diff | Borrow |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 |
Gate Breakdown
d1 = A ⊕ B (XOR1)
DIFF = d1 ⊕ Bin (XOR2)
t1 = Ā AND B (NOT1+AND1)
t2 = d̄1 AND Bin (NOT2+AND2)
BORROW = t1 OR t2