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Asked: 2026-05-17T16:52:27+00:00

I am trying to wrap my mind around how to do this. For what

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I am trying to wrap my mind around how to do this.
For what i understand is that a set of logic gates is called “functionally complete” if some combination of the gates can be used to do each of the basic logic operations AND, OR, and NOT. The claim is the NAND gate is functionally complete.

What i dont understand is how to build a OR gate as a nand gate. build a AND gate from a NAND gate etc.. would the formula i come up with have to have the same output?

 X' = X NAND 1
 X + Y = ?
 X * Y = ?

using a truth table how is X’ = X NAND 1?

I am not sure what X NAND 1 means.. I understand 1 is fixed as y?

I get confused when i see the gate inbetween 2 inputs like x NAND y

How can i construct a truth table for x+y = NAND?

or should i do it a different way?

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1 Answer

  1. Editorial Team

    Just go by definition:

    X NAND Y = ~ (X AND Y) = ~X OR ~Y

    Substitute Y = 1 and see you will get

    X NAND 1 = ~X OR ~1 = ~X OR 0 = ~X = X’

    Edit:

    Just so that you get a sense on how to build other gates using NAND gate, this wikipedia article is very good and informative. Hope it helps.

    http://en.wikipedia.org/wiki/NAND_logic

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