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I have done the problem with AND , OR and NOT gates but cant figure out how to do with NAND and NOT gates.

I dont know how to implement the NAND gate for this boolean expression.

NITIN KUMAR
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  • You can convince yourself of and use the following: `OR(a, b) = NAND(NOT(a), NOT(b))` and `AND(a, b) = NOT(OR(NOT(a), NOT(b)))` – Axel Kemper Mar 25 '23 at 14:31
  • You don't even need the `NOT` gate. You can build every logic expression with NAND alone. See for instance https://en.wikipedia.org/wiki/NAND_logic – derpirscher Mar 25 '23 at 15:01

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Using DeMorgan's Laws:

    xy    +  x'y'        +  yz
   (xy)'' + (x'y')''     + (yz)''     // all ANDs converted to NOT'd NANDs
  ((xy)'''  (x'y')''')'  + (yz)''     // first OR converted to NAND w/ args NOT'd
 (((xy)'''  (x'y')''')''   (yz)''')'  // second OR converted to NAND w/ args NOT'd
 (((xy)'    (x'y')')''     (yz)')'    // extra NOT's removed
Andrew
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