Question

Using the truth table of AND gate and NOT gate, show that NAND gate is an AND gate followed by a NOT gate. Hence write the truth table of NAND gate. Why are NAND gates called ‘Universal Gates’?

Answer 1

Hint: The AND gate and NOT gate have to be remembered with their truth table. From the truth tables, the nature of output can be known. Thereafter connect the two gates and note the outputs one by one, the required gate will be found. The final output of the two connected gates is the output of the NAND gate.
The concept of UNIVERSAL GATE is that the gate can be used to create all the gates as well as implement any logical boolean express. There are two such gates.

Complete step-by-step solution:
Truth-table of AND gate:

A(input)	B(input)	Y(output)
0	0	0
0	1	0
1	0	0
1	1	1

Truth-table of NOT gate:

A(input)	Y(output)
0	1
1	0

Now let us connect the AND and NOT gates,

Now if we see the characteristics of a NAND gate, we get the similarities with the above diagram. Such as, the NAND gate gives the output which is just the complement of any output of the AND gate.
Truth-table of NAND gate:

A(input)	B(input)	Y(output)
0	0	1
0	1	1
1	0	1
1	1	0

 Hence we can say that the NAND is the AND gate followed by NOT gate.
The symbol of the NAND gate is:

A universal gate is a logic gate that can create any Boolean function without using another type of logic gate. The NAND gate is a universal gate because you can Implement any logical Boolean function using only the NAND gate. Also, from a NAND gate, the basic gates such as OR, AND and, NOT gates can be implemented.

Note: There are two universal gates: NAND and NOR.
In practice, this is very useful since NOR and NAND gates are financial and simpler to design than other logic gates. an AND gate is generally implemented as a NAND gate followed by a NOT gate and similarly, an OR gate is generally implemented as a NOR gate followed by a NOT gate.