Page 37 - Digital Electronics by harish

4) NOR gate using only NAND gates

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

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

5) EX-OR gate using only NAND gates

Y = . B + A .

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

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

Two NAND gates are used for the two NOT functions and . Another two NAND gates are
required for . and . . A final NAND gate is required for the (.) and complement
function. Totally five NAND gates are required for realizing an EX-OR gate using only
NAND gates.

6) EX-NOR gate using only NAND 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 NAND gates. Sixth NAND gate is used to
realize the NOT gate. Totally six NAND gates are required for realizing an EX-NOR gate
using only NAND gates.

37