Half Adder in Digital Logic

Half Adder (HA):

Half adder is the simplest of all adder circuits. Half adder is a combinational arithmetic circuit that adds two numbers and produces a sum bit (s) and carry bit (c) both as output. The addition of 2 bits is done using a combination circuit called a Half adder. The input variables are augend and addend bits and output variables are sum & carry bits. A and B are the two input bits.

let us consider two input bits A and B, then sum bit (s) is the X-OR of A and B. it is evident from the function of a half adder that it requires one X-OR gate and one AND gate for its construction. 

Truth Table:

Here we perform two operations Sum and Carry, thus we need two K-maps one for each to derive the expression.

Logical Expression: 

For Sum:

Sum = A XOR B

For Carry: 

Carry = A AND B 

Implementation:

Note: Half adder has only two inputs and there is no provision to add a carry coming from the lower order bits when multi addition is performed. 

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