Makeing logic gate using only NAND Gates

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Discussion Overview

The discussion revolves around constructing logic gates using only NAND gates, specifically addressing how many NAND gates are required to replicate certain logic gate functions as depicted in a diagram. The scope includes homework-related queries and technical explanations of logic gate operations.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant states the need to create logic gates using only NAND gates and references De Morgan's Theorem.
  • Another participant questions the equivalence of expressions involving NAND gates and suggests that an inverter can be constructed from a NAND gate.
  • A participant expresses confusion about the number of inverters needed for the construction.
  • One participant points out the difference between AND and NAND gates by suggesting a comparison of their truth tables and mentions the need to apply De Morgan's Theorem for the OR gate construction.

Areas of Agreement / Disagreement

Participants appear to have differing interpretations of the logic gate constructions and the application of De Morgan's Theorem, indicating that multiple competing views remain without a consensus on the exact number of NAND gates required.

Contextual Notes

Some assumptions about the definitions of logic gates and the specific diagram referenced are not explicitly stated, which may lead to varying interpretations of the problem.

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
 

Attachments

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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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