Half Adder in Digital Logic: A Comprehensive Introduction

 

Understanding Half Adders: The Gateway 

to Binary Arithmetic

Half Adder:

A half adder is a simple digital circuit used in computer engineering and

digital electronics to perform binary addition of two single digit binary 

numbers (bits). 

It has two inputs and two outputs.

We assign symbols X and Y to the two inputs and S (for sum) and 

C (for carry) to the outputs.

X	Y	C	S
0	0	0	0
0	1	0	1
1	0	0	1
1	1	1	0

As you can see from the truth table, the sum output (S) is the XOR 

(exclusive OR) of the input bits A and B, and the carry output (C) of 

bits A and B is like AND. The truth table can be used to directly extract 

the condensed Boolean functions for the two outputs. 

The simplified sum-of-products expressions are.

                                        S = X’Y+XY’     C=XY                                           

(Comma on X or Y shows Complement)

OR    

                                                                S=X⊕Y   C=X.Y

Explanation:

- Adding “0” and “0” the Sum is “0” and carry is also “0”.   

- Adding “0” and “0” the Sum is “0” and carry is also “0”.

- Adding “1” and “0” the Sum is “1” and carry also “0”,same as previous one.

 

- Adding “1” and “1” the Sum is “0” How?   

In Boolean Algebra 1+1=2 is Represented by “10” (1 shows Carry and 0 Show 

Sum) in the table.