Page 39 - Digital Electronics by harish

4) NAND gate using only NOR gates

Y = .
= + ….. Using De-Morgan‟s second theorem, . = +

Two NOR gates are used for the two NOT functions. Another two NOR gates are required
for implementing the (+) ie. OR function. Hence, totally four NOR gates are required for
realizing a NAND gate using only NOR gates.

5) EX-OR gate using only NOR gates

Y = . B + A .

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

= . . . ….. Using De-Morgan‟s first theorem, + = .
= + + + ….. Using De-Morgan‟s second theorem, . = +

Two NOR gates are used for the two NOT functions and . Another two NOR gates are
required for (+) and complement functions. Two more NOR gates are required for the final
(+) operation. Totally six NOR gates are required for realizing an EX-OR gate using only
NOR gates.

6) EX-NOR gate using only NOR gates

Y = . + .

When the output of an EX-OR gate is connected to a NOT gate, we get an EX-NOR gate.
Hence, EX-OR gate is realized first using five NOR gates. Another NOR gate is used to
realize the NOT gate. The last two NOR gates implemented for the NOT operation can be
removed because double complementation give the same function. Totally five NOR gates
are required for realizing an EX-NOR gate using only NOR gates.

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