Derive the Boolean expression for sum and carry of half adder. Draw its combinational circuit. Implement it using only NAND gates.

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The addition of 2 bits is done using a combination circuit called a Half adder.

The truth table of half adder is

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

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

User Loaded Image | CSIT Guide

Now, we will implement circuit:

Half Adder Circuit | CSIT Guide

Now, we will implement using NAND gates

Half Adder Circuit using NAND gate | CSIT Guide

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