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Math Help - Truth Table

  1. #1
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    Truth Table

    3 MOD 4 Function

    a. Produce a truth table for a function f of four inputs, a, b, c, d that is 1 when the binary number abcd modulo 4 equals 3, and is 0 otherwise.

    b. Produce the corresponding algebraic expression for f.
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  2. #2
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    A B C D Output F
    0 0 0 0----0
    0 0 0 1----0
    0 0 1 0----0
    0 0 1 1----1
    0 1 0 0----0
    0 1 0 1----0
    0 1 1 0----0
    0 1 1 1----1
    1 0 0 0----0
    1 0 0 1----0
    1 0 1 0----0
    1 0 1 1----1
    1 1 0 0----0
    1 1 0 1----0
    1 1 1 0----0
    1 1 1 1----1

    2nd portion use K-MAP you will be able to get the solution. Hope it helps
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  3. #3
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    Never learned K-Map???? Is here other way to get the algebraic expression for the truth table.

    Would this be correct as the algebraic expression?

    f= (Ča.Čb.c.d)+(Ča.b.c.d) +(a.Čb.c.d)+(a.b.c.d)

    + = OR
    . = AND

    How do I simplify the algebraic form for f as much as possible?

    Thanks
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  4. #4
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    It is ok if have not learned K-Map. What you are doing is right. Get the minterm and simplify the expression

    f = a'b'cd + a'bcd + ab'cd + abcd
    f = a'cd(d+d') + acd(b' + b)
    f = a'cd +acd
    f = cd(a'+a)
    f = cd

    Using K-Map is much faster but there are certain limitations. You might want to look at that when you have the time.

    Karnaugh map - Wikipedia, the free encyclopedia

    Hope it helps
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