Adders are important in computers and also in other types of digital systems in which numerical data are processed. An understanding of the basic adder operation is fundamental to the study of digital systems. In this article, the half-adder and the full-adder are introduced.


The Half-Adder

A half-adder adds two bits and produces a sum and an output carry.

Recall the basic rules for binary addition:


The operations are performed by a logic circuit called a half-adder.

The half-adder accepts two binary digits on its inputs and produces two binary digits on its outputs a sum bit and a carry bit.

A half-adder is represented by the logic symbol:

Half-Adder Logic

From the operation of the half-adder as stated in Table , expressions can be derived for the sum and the output carry as functions of the inputs. Notice that the output carry (Cout) is a 1 only when both A and B are 1s; therefore, Cout can be expressed as the AND of the input variables.



Now observe that the sum output (Σ) is a 1 only if the input variables, A and B, are not equal. The sum can therefore be expressed as the exclusive-OR of the input variables.

From Equations , the logic implementation required for the half-adder function can be developed. The output carry is produced with an AND gate with A and B on the inputs, and the sum output is generated with an exclusive-OR gate, as shown in Figure . Remember that the exclusive-OR can be implemented with AND gates, an OR gate, and inverters.
Half-adder logic diagram.