A 4bit ripple carry adder consists of one half adder and three full adder. A half adder has two inputs (a and b), least significant bits (LSB) of each operand, and two outputs, sum and carry. A full adder has one additional input, cin, carry input from the lower bit. In a half adder, two outputs are given by the following formulas:
where @ and * stand for Exclusive-Or and And in XDE's notation respectively. In a full adder, outputs are given as follows:
where + stands for Or in XDE. carry is first generated at LSB and propagated to MSB. Hence this type of adder is called ripple carry. By connecting carry and cin of these half adder and full adders we can configure a 4bit adder.
