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Math Help - basic boolean logic

  1. #1
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    basic boolean logic

    Hello, I just want to confirm a few boolean logic questions.

    1. Both the inputs to a NOR gate are A the output will be :
    A / NOT A / unknown.
    I think the answer should be "NOT A".

    2. If a three input NAND gate has two inputs connected to a +5V and the third input to A, the output will be:
    A / NOT / unknown
    I think the answer should be "NOT".

    3. If one input to a NOR gate is HIGH and the other inputs are unknown, but could be either HIGH or LOW, the output is:
    HIGH / LOW / UNKNOWN
    I think the answer is "LOW".

    Thank you for any confirmation that I am on the right track.
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  2. #2
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    Re: basic boolean logic

    Hey, I worked it myself and I got the same answers.

    Number 2 is NOT A, right?
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  3. #3
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    Re: basic boolean logic

    Quote Originally Posted by jll90 View Post
    Number 2 is NOT A, right?
    Does +5V mean True from the standpoint of logic? Then yes, the answer is NOT A. True AND True AND A = A, so NOT (True AND True AND A) = NOT A (assuming I understand correctly what a three-input NAND gate is).
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  4. #4
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    Re: basic boolean logic

    In terms of boolean algebra:
    i). The output of a NAND gate with inputs a, b is \overline{ab}=\overline{a}+\overline{b}

    ii). The output of a NOR gate with inputs a, b is \overline{a+b}=\overline{a}\overline{b}

    1. A and A into a NOR gate yields \overline{A}\,\overline{A}=\overline{A} = not A

    2. Does a+5V mean the output of running a through an inverter? If so, the 3 inputs to the NAND gate are \overline{a}, \overline{a}\,\, and A and then output
    \overline{A}+\overline{\overline{a}}+a=\overline{A  }+a Is there unstated relationship between a and A, for example A=\overline{a}. If so, the answer is a, otherwise unknown.

    3. Any relationship between LOW and HIGH, e.g. HIGH=\overline{LOW} ? If so, output is
    \overline{HIGH}+\overline{X} with X either HIGH or not HIGH. But even here, you get unknown.

    I think the best way to deal with the logical gates is with boolean algebra. I hope your instructor or text book is more explicit on exactly what the situation is.
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