Digital Eectronics - Adder

          In electronics, an adder or summer is a digital circuit that performs addition of numbers. In many computers and other kinds of processors, adders are used not only in the arithmetic logic unit(s), but also in other parts of the
processor, where they are used to calculate addresses, table indices, and similar operations.

Types Of Adder

• Half Adder.
• Full Adder.
• Ripple Adder.
• Carry-Save Adder.

Half Adder adds two single binary digits A and B. It has two outputs, sum (S) and carry (C). The carry signal represents an overflow into the next digit of a multi-digit addition. The value of the sum is 2C + S. The simplest half-adder design, is made up of an XOR gate for S and an AND gate for C. With the addition of an OR gate to combine their carry outputs, two half adders can be combined to make a full adder.

The half adder adds two input bits and generates a carry and sum, which are the two outputs of a half adder. The input variables of a half adder are called the Augend and Addend bits.The output variables are the sum and carry. The truth table for the half adder is :

 

Full adder adds binary numbers and accounts for values carried in as well as out. A one-bit full adder adds three one-bit numbers, often written as A, B, and C_in; A and B are the operands, and C_in is a bit carried in from the previous less significant stage^. 

The full adder is usually a component in a cascade of adders, which add 8, 16, 32, etc. bit binary numbers. The circuit produces a two-bit output, output carry and sum typically represented by the signals C_out and S, where . The one-bit full adder's truth table is: