Binary adder

CategoriesSee also FPU GPU AGUMechanical calculatorAn adder, or summer, is a digital circuit that performs addition of numbers. In many computers and other kinds of processors, adders are used in the arithmetic logic units (ALUs). They are also used in other parts of the processor, where they are used to calculate addresses, table indices, increment and decrement operators and similar operations. Although adders can be constructed for many number representations, such as binary-coded decimal or excess-3, the most common adders operate on binary numbers. In cases where two's complement or ones' complement is being used to represent negative numbers, it is trivial to modify an adder into an adder–subtractor. Other signed number representations require more logic around the basic adder. HistoryGeorge Stibitz invented the 2-bit binary adder (the Model K) in 1937. Binary addersHalf adderThe half adder adds two single binary digits A{\displaystyle A} and B{\displaystyle B}. It has two outputs, sum (S{\displaystyle S}) and carry (C{\displaystyle C}). The carry signal represents an overflow into the next digit of a multi-digit addition. The value of the sum is 2C+S{\displaystyle 2C+S}. T