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Math Help - Half-adder with NAND gates

  1. #1
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    Half-adder with NAND gates

    Show a half-adder with only NAND gates.

    I knew for half-adder that c = xy and s = xNORy

    I feel like this will become a never ending cycle of putting double bars and making
    NOTx = xNANDx

    Thanks!
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  2. #2
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    You can make NOT gates from NAND.
    So you can make AND gates from NOT and NAND.
    Now, you can make OR gates from NOT and AND (use DeMorgan's)

    Now you can make anything. Won't be an endless cycle, because the above list of gate dependencies is not circular.
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  3. #3
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    Yes, i can make OR gates from NOT and AND.

    When I want to get OR back to NAND, however, I need to double bar so I can use a bar in DeMorgan's to get NAND back.
    Then, I am left with one bar, which I need to get rid of by making NOT and AND an OR gate.

    I am then back where I started.
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  4. #4
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    x OR y = NOT(NOT x AND NOT y) = NOT x NAND NOT y
    = (x NAND x) NAND (y NAND y)

    right?
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