ADDERS AND SUBTRACTORS

Half Adder

The half adder is an arithmetic circuit used to perform the addition of two single bits. The two input variables to the half adder designate the augend and addend bits and the output variables produce the sum and carry. Let A and B are the two input variables and sum (S) and carry (C) are the two output variables. Then,

Full Adder

A full adder is a combinational circuit that performs the arithmetic sum of three input bits. It consists of three input variables designated by augend, addend and the input carry bit. The two output variables produce the SUM and CARRY. Let the two input variables are denoted by A and B, represent the two significant bits to be added. The third input Ci represents the carry from the previous lower significant position. The two outputs are sum (S) and carry (Ci + 1).

Half Subtractor

A half subtractor is a combinational circuit that subtracts one bit from the other and produces the difference. A half subtractor circuit with two input variables designated as A (minuend) and B (subtrahend); and output variables as Difference ‘D’ and Borrow ‘b’ is shown in the figure below.
Here, the operation A minus B is performed. The borrow output ‘b’ will be ‘1’ whenever A < B. If A < B, then subtraction is done by borrowing 1 from next higher order bit.

Full Subtractor

A full subtractor is a combinational circuit which performs subtraction involving three bits, namely minuend bit, subtrahend bit and the borrow from the previous stage. The three inputs are A(mineund), B(subtrahend) and bi(borrow from the previous stage) and two outputs D(difference) and bi + 1(borrow out) as shown in figure.