Half Adder

The addition of 2 bits is done using a combination circuit called a Half adder. The input variables are augend and addend bits and output variables are sum & carry bits. A and B are the two input bits. Truth Table:

Here we perform two operations Sum and Carry, thus we need two K-maps one for each to derive the expression.

Logical Expression:

1) for Sum:                              

Sum = A XOR B

2) for Carry:                                

Carry = A AND B

Implementation:

Note:

Half adder has only two inputs and there is no provision to add a carry coming from the lower order bits when multi addition is performed.