Design a 1 bit halfadder that will output the sum and carry

Design a (1 bit) half-adder that will output the sum and carry. Remember, a half-adder contains two inputs (two 1-bit binary numbers) and two outputs (again, two 1-bit binary numbers).

Include:

1) Truth Table

2) Kmap

3) Simplified expression of the original expression

Solution

1)Truth table : 1 bit addition

a b sum carry

0 0 0 0

0 1 1 0

1 0 1 0

1 1 0 1

here...............................a and b are inputs......................................................

....................sum and carry are outputs.................................................

2)k-map: with the help of k-map the following are obtained

for(i) sum= a\'b+b\'a

(ii)carry=a.b

3) simplified exprassion of the original expression: (i) for sum=a xor b

Note:It is nothing but an xor operation.

(ii)carry=a.b