Half Adder

Half Adder

The half adder :

·         Add two single binary digits (eg: A and B)

·         Produce two outputs which are  sum (∑) and carry out  (C_out)

·         The sum is the low order output and the carry out is the high order output…

The logic symbol for Half adder:

(A and  B are the input bits ; while sum carry are the output )

Each  bit from A and B is added together like binary operations;

o   0 + 0 = 0

o   0 + 1 = 1

o   1 + 0 = 1

o   1 + 1 = 0   (because 1+ 1 =1=10₂ so ;

                    1 become the carry bit ;

                    then as concluded ∑=0 and C_out = 1)

Below is the truth table of half adder:

A	B	Cout	∑
0	0	0	0
0	1	0	1
1	0	0	1
1	1	1	0

Then ,we need to find out the equation to represent the function of sum (∑ ) and the carry out (C_out) through using Karnaugh Map;

Sum:

A B	A’	A
B’	0	1
B	1	0

Through this Karnaugh Map,

SOP of the sum = AB’ + A’B

Then the equation of sum , ∑;

∑ =A’B + A’B

OR

∑ = A  xor B  (XOR gate)

For  carry out , C_out ;

A        B	A’	A
B’	0	0
B	0	1

From the Karnaugh Map;

The equation of carry out , C_out ;

C_out =  A.B (AND gate)

Finally, logic diagram for half adder can be derived from the simplified functions:

Chong Cai Ning B031210080