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# Basic Arithmetic Logic Unit (ALU) Circuitry

One of the primary functions performed by a computer is mathematics. Even functions like graphics and sorting data are mathematics - because everything on a computer is represented by digital data. This article describes the digital logic circuits used to perform binary addition and subtraction.

 A B Sum Carry 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1

The circuit shown above and its accompanying logic diagram performs the function of adding two one-bit binary numbers. The output of the circuit provides the sum along with a possible carry. When adding higher-bit binary numbers however, provisions for a carry-in from a previous stage must be provided. For this reason, this circuit is called a "half-adder".

In the circuit shown above, a second stage has been added to accept a carry-in from a previous stage. The carry-out of this circuit is created by ORing the carry bits of both stages. This circuit is called a "full-adder".

 A B C Sum Carry 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1

Logic diagram of the full adder.

To simplify circuit diagrams we could indicate a full adder using a simple box labeled with the circuit's function and with its inputs and outputs labeled.

By connecting eight full-adder circuits together, each circuit's carry-out output to the carry-in input of the next circuit, we can construct an eight-bit binary adder.

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