The logic graph below shows the eight different cases that may be encountered when adding two binary numbers. Once a circuit that can add any pair of bits has been designed, that circuit can be replicated N times to create an N-bit adder. By focusing on the requirements for adding a single pair of bits from two N-bit binary numbers, an otherwise complex design challenge can be divided into a more tractable problem. Like any circuit that deals with signals grouped as binary numbers, the simplest adding circuit can most easily be designed using the bit-slice approach. The simplest adding circuit performs addition in much the same way that humans do, performing the operation right to left, bit-by-bit from the LSB to the MSB. The basic adding circuit is one of the cornerstones of digital system design, and it has been used in countless applications since the earliest days of digital engineering.
Adder circuits add two N-bit operands to produce an N-bit result and a carry out signal (the carry out is a ‘1’ only when the addition result requires more than N bits).
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