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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.

Half adder circuit


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".

Full adder circuit

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".


Logic diagram of the full adder.

Adder circuit

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.

Eight-bit binary adder

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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