Design half adder using NAND gates only. Also draw the diagram.

Q.) Design half adder using NAND gates only. Also draw the diagram.
Subject: Digital Systems

A half adder is a type of adder, an electronic device that performs the addition of numbers. The half adder is able to add two single binary digits and it provides the output as well as a carry value. It has two inputs, known as the augend and addend bits, and two outputs, the sum (S) and carry (C) bits. The basic representation of a half adder is shown below:

  Inputs: A, B
  Outputs: Sum (S), Carry (C)

The truth table for a half adder is:

A	B	Sum (S)	Carry (C)
0	0	0	0
0	1	1	0
1	0	1	0
1	1	0	1

From the truth table, we can derive the following Boolean expressions for Sum and Carry:

Sum (S) = A XOR B
Carry (C) = A AND B

However, the question asks us to design the half adder using only NAND gates. A NAND gate is a universal gate, which means we can construct any other gate using only NAND gates.

The NAND gate equivalent for XOR (A XOR B) and AND (A AND B) gates are as follows:

XOR gate using NAND gates:

A XOR B = (A NAND (A NAND B)) NAND (B NAND (A NAND B))

AND gate using NAND gates:

A AND B = (A NAND B) NAND (A NAND B)

Now, we can design the half adder using these expressions. The circuit diagram would look like this:

  A ----&gt; |NAND| ----&gt; |NAND| ----&gt; |NAND| ----&gt; Sum
          |    |       |    |       |    |
  B ----&gt; |NAND| ----&gt; |NAND| ----&gt; |NAND|
          |    |       |    |
  A ----&gt; |NAND| ----&gt; Carry
          |    |
  B ----&gt; |NAND|

In the above diagram, the first two NAND gates are used to generate the XOR operation for the Sum output. The last two NAND gates are used to generate the AND operation for the Carry output.

This is how we can design a half adder using only NAND gates.