need help with boolean equations ASAP!

Discussion in 'Homework Help' started by stressout, Jan 22, 2011.

  1. stressout

    Thread Starter New Member

    Jan 22, 2011
    2
    0
    1. Prove the identity of the boolean equation ab + bc'd + a'bc + c'd = b +c'd using algebraic equations.

    2. Simplify the logic functions xyz + x'y + xyz'x' + xy + xz' +xy'z' using boolean algebra rules
     
  2. stressout

    Thread Starter New Member

    Jan 22, 2011
    2
    0
    i have try the first question. Is it correct??? any simpler way.. i mean short way.. this is long..

    RHS
    b +c'd
    = b (1+a) + c'd
    = b + ab + c'd
    = (a+a')b + ab + c'd
    = ab + a'b + ab + c'd
    =ab + a'b (c+c') + ab + c'd
    =ab + a'bc + a'bc' + ab + c'd
    =ab + a'bc + b (a'c' +a) + c'd
    =ab + a'bc + b(c' (a'+a) + c'd
    =ab + a'bc + b(c') + c'd
    =ab + a'bc + bc' + c'd
    =ab + a'bc + bc'(d+d') + c'd
    =ab + a'bc + bc'd + bc'd' + c'd
    =ab + a'bc + c'd(b+1)+ bc'd'
    =ab + b'c'd' + a'bc +c'd
     
  3. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    The first exercise is wrong and its two parts aren't equal. The correct exercise should be ab+bc'd+a'b+c'd=b+c'd. You can work this out easilly if you group first the c'd factors together.

    Try an attempt for the second one too. Remember that xx'=0 and (x+x')=1.
     
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