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Reducing Boolean algebra

Discussion in 'General Electronics Discussion' started by cps13, Feb 25, 2013.

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  1. cps13

    cps13

    41
    1
    Feb 25, 2013
    Hi,

    I am new to the forum so hello to all.

    I am studying a BTEC in EE and going onto a HND hopefully next year. I am struggling a bit with reducing boolean algebra. I seem to be able to look at the same problem 3 times and come up with three different answers.

    Can someone give me some hints. If some is NOT for example NOT A I write it as A'

    I have this problem.... ABC + A'B'C' + ABC' + A'C'

    this is one way I have "solved" it.

    ABC + A'B'C' + ABC' + A'C'
    ABC + A'B'C' + ABC' + A' . 1 (last C' cancelled against first C, turns into 1 (A+A' = 1))
    AB + A'B'C' + C' + A' . 1 (cancelled first AB against second AB in third group)
    AB + A'B'C' + A' . 1 (cancelled second C' as same as C' in second group)
    AB + B'C' + A' . 1 (A' in second group removed as same as last A')
    AB + B'C' + A' (A' . 1 = A')

    Any help would be greatly appreciated!

    Thanks!
     
  2. john monks

    john monks

    693
    2
    Mar 9, 2012
    I cannot figure out how to answer your question other than to do your homework for you.
    If worst comes to worst draw up a truth table and figure it out.
    You probably should look at the Tutorial entitled "Converting Truth Tables into Boolean Expressions"
     
  3. cps13

    cps13

    41
    1
    Feb 25, 2013
    Are you able to explain to me how you would get the correct answer? Rather than just write the correct answer. Or if my answer is wrong where I have gone wrong?

    I have read sections from two text books but I am still struggling. I cannot draw up a truth table to solve it because the exercise is to reduce a boolean expression using de-morgans theorum, boolean postulates etc...
     
  4. (*steve*)

    (*steve*) ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd Moderator

    25,496
    2,837
    Jan 21, 2010
    OK, here's a hint that might get you started.

    Look at ABC + ABC' -- Can you simplify that in your head?

    You can't just cancel things willy nilly.

    ABC + ABC' = AB(C + C') And C+C' = ?
     
  5. john monks

    john monks

    693
    2
    Mar 9, 2012
    Your mistake was in your first step. Steve caught it.
    You misapplied the Identity Law AB + AB' = A.
    My physics professor drove a point home with me that if you cannot derive a formula you should not be using it. I don't understand why your professor placed such constraints on you by using only de-morans theorum, bolean postulates etc. but I can say one thing for sure. You should go through and prove de-morgans theorum and all the relevant boolean postulates. You can do it by using a truth table.
    Then and only then should you use them.
     
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