What is the combinational circuit called which is used to subtract one binary number from another?

The combinational circuit used to subtract one binary number from another is called a "Subtractor".

A subtractor is a digital circuit that performs subtraction of numbers. The subtractor is classified into two types: Half subtractor and Full subtractor.

1. Half Subtractor: A half subtractor is a combinational circuit that subtracts two bits and produces their difference and borrow. It has two inputs, called minuend and subtrahend, and two outputs, called difference and borrow.

The truth table for the Half Subtractor is:

| Minuend (A) | Subtrahend (B) | Difference (D) | Borrow (Bo) | |-------------|----------------|----------------|-------------| | 0 | 0 | 0 | 0 | | 0 | 1 | 1 | 1 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 0 |

The formulas for Difference and Borrow are:

Difference (D) = A XOR B

Borrow (Bo) = A' AND B

1. Full Subtractor: A full subtractor is a combinational circuit that performs subtraction involving three bits: two minuend bits and a borrow bit. It has three inputs: A (minuend), B (subtrahend), and Bin (borrow in), and two outputs: D (difference) and Bout (borrow out).

The truth table for the Full Subtractor is:

| A | B | Bin | D | Bout | |---|---|-----|---|------| | 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 |

The formulas for Difference and Borrow are:

Difference (D) = A XOR B XOR Bin

Borrow (Bout) = (A' AND B) OR (Bin AND (A XOR B))

In digital electronics, the subtractor is used in various computational and mathematical operations. For example, the operation of a digital calculator to perform subtraction, the operation of decrementing the value of a binary counter, etc.