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# Full Adder Circuit

GCSE Computer Science requires that you know about the ALU (Arithmetic Logic Unit) in the CPU, the symbols and outputs of logic circuits, and how to perform binary addition. Are these three unrelated pieces of knowledge, or are they linked?

You might have guessed (from its name), that additions (and other calculations) are performed in the Arithmetic Logic Unit. How does the ALU perform the additions? Using logic circuits.

This page shows how a full adder circuit can be constructed to add binary digits. The three bits on the left are the bits to be added - you can click to toggle them. The bottom bit represents the bit carried into the calculation from the column immediately to the right (i.e. that containing the digits that are one place less significant), and is sometimes labelled Cin. The digits on the right, S and C are the result of the addition, which can also be seen below the circuit. The digits shown inside the circuit are the intermediate values at those points.

0
0
0
0
0
0
0
0
0 + 0 = 00

Note that in this circuit, S is the sum of the two digits, and C (sometimes known as Cout) is the value to be carried. This value would become the Cin value for the digits in the column to the left (i.e. one place more significant).

This circuit uses AND, OR and Exclusive-OR (also known as EOR or XOR) gates/operators - you can see the truth tables for those operators here. There will be other ways of making an equivalent circuit. There is also a similar circuit called a half adder which performs the addition on two bits without the bit carried in. Logic circuits can also be used for other operations, such as comparison.