Arithmetic Circuits and the Arithmetic Logic Unit

Arithmetic circuits are digital logic networks that perform numerical operations on binary data. They are built from basic logic gates, AND, OR, NOT, NAND, NOR and XOR, combined to implement addition, subtraction, multiplication and comparison. Because computers represent numbers in binary, these circuits manipulate strings of bits according to the rules of binary arithmetic, and they form the computational core of processors and many other digital systems.

The building block of binary addition is the adder. A half adder sums two bits and produces a sum and a carry, while a full adder also accepts an incoming carry, allowing single-bit adders to be chained to add multi-bit numbers. Subtraction is usually performed by adding the two's complement of a number, so the same adder hardware handles both operations. Multiplication is implemented as a sequence of shift-and-add steps or with dedicated array structures, following a multiplication algorithm that builds the product from partial products.

These circuits are gathered together in the arithmetic logic unit (ALU), the part of a processor that carries out arithmetic and logical operations. The ALU takes operands and a control code selecting the operation, and produces a result along with status flags such as carry, zero and overflow. ALUs and other digital functions are commonly realised in CMOS logic and may be integrated into application-specific integrated circuits (ASICs), where many such functions are combined on a single custom chip.

Frequently asked questions

What is the difference between a half adder and a full adder?

A half adder adds two bits and outputs a sum and carry. A full adder also takes a carry input, so full adders can be cascaded to add multi-bit binary numbers.

How is subtraction done in digital circuits?

Subtraction is usually carried out by adding the two's complement of the number to be subtracted, which lets the same adder hardware perform both addition and subtraction.

What does an ALU do?

The arithmetic logic unit performs the arithmetic and logical operations of a processor, selected by a control code, and reports status flags such as carry, zero and overflow.