Logic Diagram assistance

Discussion in 'Homework Help' started by christophero, Oct 13, 2009.

  1. christophero

    Thread Starter New Member

    Oct 13, 2009
    2
    0
    My situation is that I have this expression that I must convert to a logic diagram, the expression is Z = (A not + B not x C) x (A not + B not x C).

    May I get how this expression is layed out in a logic diagram, I am able to use NOR and NAND gates.
     
  2. Ratch

    New Member

    Mar 20, 2007
    1,068
    3
    christophero,

    The first thing you should do is to write your logic expressions using concise notation like A'+BC+(A+C), where an apostrophe denotes negation. Then simplify your expression using a Karnaugh map. Afterwards, it is a trival operation to lay out the logic chips. You can make any logic expression using NOR gates exclusively or NAND gates exclusively. There are methods to convert any logic expression to all NORs or all NANDs. The same cannot be said of ANDs and ORs, because no matter how clever you are, there is no way to make an AND or an OR invert an input.

    Ratch
     
  3. Thav

    Member

    Oct 13, 2009
    82
    0
    Something helpful after you've gone through simplifying is the conversion from positive logic gates to negative logic gates.

    For instance take an AND gate truth table.
    A B X
    0 0 0
    0 1 0
    1 0 0
    1 1 1
    Now consider a NOR gate truth table
    A B X
    0 0 1
    0 1 0
    1 0 0
    1 1 0
    Now consider the truth table of a NOR gate with both inputs inverted.
    A B X
    0 0 0
    0 1 0
    1 0 0
    1 1 1
    Familiar, isn't it? The same relationship applies to OR and NAND, but I'll let you work that one out. This technique can be used to simplify schematics with a lot of not gates + positive logic, or can help you utilize all negative logic (which is faster due to the internal transistor layout of these gates)

    Ratch's recommendation to simplify using K-maps is a great start because the intermediate stages really don't matter here as long as the output is correct.
     
  4. christophero

    Thread Starter New Member

    Oct 13, 2009
    2
    0
    What I recieved after involving the professor was Z = A' It was derived from foiling the expression and then working it out. Thank you for the assistance with the explainations.

    Chris
     
  5. LKjell

    New Member

    Oct 17, 2009
    6
    0
    Z = (A not + B not x C) x (A not + B not x C)
    Z = (A' + B'C)(A' + B'C)
    Z = A'+ B'C

    But you said that your answer is Z = A'. Therefore there has to be a misunderstanding somewhere. Anyway to turn this into NAND/NOR gates we use De Morgan's laws.

    Z = (A' + B'C)''
    Z = (A(B'C)')'
     
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