1. sneha

2.  A combinational circuit that performs the addition of two bits is called a half adder.  It has two inputs.  It has two outputs.

3.  Truth table:  X Y | C S  -------------  0 0 | 0 0  0 1 | 0 1  1 0 | 0 1  1 1 | 1 0 Half adder X Y C S

5.  A full adder is a combinational circuit that performs the sum of three bits(two significant bits and a previous carry).

6. Truth table: X Y Cin | C S ------------------- 0 0 0 | 0 0 0 0 1 | 0 1 0 1 0 | 0 1 0 1 1 | 1 0 1 0 0 | 0 1 1 0 1 | 1 0 1 1 1 | 1 0 1 1 1 | 1 1 Full adder Cin X Y S C

7.  Truth table:  Using K-map, simplified SOP form is: C = XY + XZ + YZ S = X'Y'Z + X'YZ'+XY'Z'+XYZ 1 01 10 00 YZ 0 01 10 01 11 10 X 1 00 01 00 YZ 0 11 01 01 11 10 X SumCarry S =  m(1,2,4,7) C =  m(3,5,6,7) 0 1 3 2 0 1 3 2 4 5 7 6 4 5 7 6 Z

8.  Using K-map, simplified SOP form is: C = XY + XZ + YZ S = X'Y'Z + X'YZ'+XY'Z'+XYZ

9.  Circuit for above formulae: C = XY + (X  Y)Z S = X  Y  Z XYXY S C Z (XY) (X  Y). Circuit Diagram

10. 10 Half Adder Cin Cin + xy