Makeing logic gate using only NAND Gates

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To create logic gates using only NAND gates, one can utilize De Morgan's Theorem to derive the necessary configurations. An inverter can be constructed from a single NAND gate, which simplifies the design of AND and OR gates. For an AND gate, the expression A.B can be represented as (A' + B')', while an OR gate can be expressed as (A + B)'' using NAND gates. The discussion emphasizes comparing truth tables to understand the differences between AND and NAND gates. Overall, the key takeaway is that NAND gates can be used to construct any logic gate through careful application of inversion and De Morgan's principles.
ronybhai
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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
 

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

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