sneha
A combinational circuit that performs the addition of two bits is called a half adder.
It has two inputs. It has two outputs .
Truth table: X Y | C S ------------- 0 0 | 0 0 0 1 | 0 1 1 0 | 0 1 1 1 | 1 0
Half adder
XY
C S
A full adder is a combinational circuit that performs the sum of three bits(two significant bits and a previous carry).
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
SC
Truth table:X Y Z 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 0 1 0 1 1 1 1 1
Using K-map, simplified SOP form is:
C = XY + XZ + YZ
S = X'Y'Z + X'YZ'+XY'Z'+XYZ
10 11 0
00 YZ 0
0 11 0
01 11 10
X 1
0 00 1
00 YZ 0
1 10 1
01 11 10
XSum Carry
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
Using K-map, simplified SOP form is:C = XY + XZ + YZS = X'Y'Z + X'YZ'+XY'Z'+XYZ
Circuit for above formulae:
C = XY + (XY)Z
S = XYZ
XY S
C
Z
(XY)
(XY)
.
Circuit Diagram
10
Half Adder Half Adder
Cin
Cin
Cin
Cin + xy