A **subtractor** is a digital logic circuit in electronics that performs the operation of subtraction of two number. Subtractors are classified into two types: half subtractor and full subtractor.

A **full subtractor (FS)** is a combinational circuit that performs a subtraction between two bits, taking into account borrow of the lower significant stage. This circuit has three inputs and two outputs. The three inputs are A, B and C, denote the minuend, subtrahend, and the previous borrow, respectively. The two outputs are the difference (A−B−C) and borrow.

The truth table of the full subtractor Circuit is shown in figure 2.

### Implementation of Full Subtractor

Logical expression for Difference,

Logical expression for borrow,

The FS works by combining the operations of basic logic gates, with the simplest form using one **XOR**, one **OR**, one **NOT** & three** AND** gate.

**Note:**

1. FS can be implemented with two half subtractor and one OR gate.

2. Minimum number of NAND Gate required implementing FS = 9

3. Minimum number of NOR Gate required implementing FS = 9

4. FS can be implemented by a combination of one **3×8 decoder** and two **OR** gate.