Subtractor

A subtractor is a digital logic circuit that performs subtraction of binary numbers. It is the counterpart of an adder and is used in arithmetic units of processors and other digital systems. The circuit takes one or more minuend bits, subtrahend bits, and, for multi-bit subtraction, a borrow input, and outputs a difference bit along with a borrow signal.

The basic building blocks are the half subtractor and the full subtractor. A half subtractor accepts two inputs, A (the minuend) and B (the subtrahend), and produces Difference D = A XOR B and Borrow B_out = NOT A AND B. A full subtractor accepts A, B, and a borrow-in Bin. It yields D = A XOR B XOR Bin and Bout = (NOT A AND B) OR (Bin AND (NOT A OR B)). These can be chained to perform subtraction of multi-bit numbers, producing the final borrow-out.

Implementation and variations: In hardware, subtractors are built from logic gates. They can also perform subtraction by using an adder with the subtrahend complemented and an initial borrow-in of 1, i.e., A + (~B) + 1. This approach allows reuse of existing adder designs. Subtraction is often performed as two's complement addition in modern architectures. Subtractors can be arranged in ripple-borrow or look-ahead configurations to optimize speed.

Analog subtractors: In analog electronics, subtractor circuits using operational amplifiers create a difference between two input voltages. A common topology is the subtractor or differencing amplifier, which yields an output proportional to the difference of the inputs according to a resistor network.

See also: adder, arithmetic logic unit, two's complement, differential amplifier.