Sneha. A combinational circuit that performs the addition of two bits is called a half adder. It...

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