Boolean tricky problems !!

Discussion in 'Math' started by HMHQ8, Jan 30, 2008.

  1. HMHQ8

    Thread Starter Member

    Jan 29, 2008
    10
    0
    Hi Guys,

    I have some boolean problems, and if you can solve it ... just do it ;)

    1)Write the dual of each Boolean expression. (Insert parentheses so that the result is properly interpreted.)

    a) A + B . C

    b) A . (B + C’) + (A’(B . C)’

    c) A + B + (A + B)’ .C + (A + B + C)’ . D


    _______________________________________________


    2) Use the axioms and theorems of Boolean algebra to prove the following theorems.

    a) (A . B) + (A . B’) = A

    b) (A . B) + (A’ . C) + (B . C) = A’ . C

    c) AB’ + A’B = (A + B) . (A’ + B’) = (A + B) . (AB)’

    d) A + A’ . B . C = A + B . C


    _______________________________________________


    3) The following expressions are difficult to read as written. Insert Parentheses to clarify them by identifying the operator hierarchy in each function.

    a) A + B’. C + D’ . E

    b) A . B + C . D + E + F

    c) A . B + C . (D + E . F)’


    ________________________

    Let us share the solution :)
     
  2. chesart1

    Senior Member

    Jan 23, 2006
    269
    1
    The dual equation can be obtained by replacing the following:
    + with .
    . with +
    0 with 1
    1 with 0

    The principle of duality does not mean that the dual equation must equal the original equation. However, the dual equation must be valid for all values of it's variables.

    Example: The dual of:
    A + A' = 1
    is
    A . A' = 0

    However the dual of
    A + B = 1
    is not
    A . B = 0
    because if A = 1 and B = 1, then A . B is not equal to 0. Therefore A . B = 0 is not a valid equation.

    If you need a clear explanation of any other concept, ask.

    If you accept a job in engineering, then understanding these concepts may be important. Boolean algebra can be used to design some digital circuits. Sometimes a circuit designed with boolean algebra yields less components than the same circuit designed without boolean algebra. You are making a mistake trying to have someone else do your homework for you.
     
  3. HMHQ8

    Thread Starter Member

    Jan 29, 2008
    10
    0
    Thank you for your support. The problem is that I didnt understand the boolean algebra as I think I should do,, what I mean is I need to know how I can deal with boolean problems, knowing the solution key is the most important thing that I need. However, I did solve these problems but I need to double check the answer.

    So, can I show you my answers to correct them or maybe you can tell me how I can do them well.

    Thank you again, and really in these days I need some one who can leed me to the correct direction in boolean algebra. :)
     
  4. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
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