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Design circuit with Minimum NOR

Before seeing the chapter please follow the previous chapter: 

Design circuit with Minimum NAND gate, Important points

Like NAND gate (two-level AND OR hierarchy) same way, if we try to implement any circuit by NOR then try to write it POS order because POS is two level of OR – AND hierarchy.

Example: 

How many minimum 2 inputs NOR gate will be required to implement (A + B) (C + D).

Solution: 

This circuit is POS (Product of Sum) means two-level of OR – AND hierarchy.

Now because it is a two-level of OR – AND hierarchy we can easily convert it by NOR. 

First, we can put  the ‘not’ bubble in two-level of OR and then cancel it by putting a double bubble at AND gate.

Now we know:

Here double bubble AND is equal to NOR.

Then we can write,

So, minimum three (3) NOR gate is required to implement (A + B) (C + D).