Page 36 - Digital Electronics by harish

1.4.3 Realization of gates using universal gates
We can use only NAND gates for constructing all the other gates (ie. NOT, OR, AND, NOR,
EX-OR and EX-NOR). Similarly, we can useonly NOR gates for constructing all the other
gates. Hence, NAND and NOR gates are called universal gates.

Realization of gates using NAND gates only

1) NOT gate using only NAND gates

Y =
= ( . ) ……. Because A . A = A

Hence, when we tie the two inputs of an NAND gate together we get a NOT gate.

2) OR gate using only NAND gates

Y = A + B
= + ……. Double complementation will give the same function
= . ….. Using De-Morgan‟s first theorem, + = .

Two NAND gates are used for the two NOT functions. A third NAND gate is used for the (.)
and complement functions.

3) AND gate using only NAND gates

Y = A . B

= . ……. Double complementation will give the same function

One NAND gate is used for the . function. Another NAND gate is used for the
complement function.

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