Makeing logic gate using only NAND Gates

[ronybhai]

Homework Statement

How to make a logic gates only using NAND gates of the following diagram.
How many NAND gates I would have to use for that diagram

Homework Equations

The Attempt at a Solution

I know that A bar bar + B bar bar =AB
A bar bar B bar bar = A+B
De-morgans Theorem

 

[CWatters]

I know that A bar bar + B bar bar =AB

Does it? I would write...

A.B = (A.B)'' = (A'+B')'

so using your notation I make it..

A.B = (A bar + B bar) bar

As for the actual question... Remember you can make an inverter from a NAND gate.

 

[ronybhai]

how many inverter I wud hve to use...little confusing I guess

 

[CWatters]

Look at the top gate. It's an AND gate right, so what's the difference between an AND and a NAND? Compare the truth tables if necessary.

As for the other gate...

It's an OR gate (eg the OR/NOR family rather than the AND/NAND family) so that's a clue you will need to apply demorgan ..

A+B
which is the same as..
= (A+B)''
because Inverting twice has no effect. Then apply demorgan and see what you get.