cant understand boolean algebra for the life of me!

Discussion in 'Homework Help' started by Maxoriley618, Sep 9, 2012.

  1. Maxoriley618

    Thread Starter New Member

    Sep 9, 2012
    13
    0
    Determine whether or not the following expressions are valid, i.e., whether the left- and
    right-hand sides represent same function.
    (a) x1'x3 + x1x2x3' + x1'x2 + x1x2' = x2'x3 + x1x3' + x2x3' + x1'x2x3
    (b) x1x3' + x2x3 + x2'x3' = (x1 + x2' + x3)(x1 + x2 + x3')(x1' + x2 + x3')
    (c) (x1 + x3)(x1' + x2' + x3')(x1' + x2) = (x1 + x2)(x2 + x3)(x1' + x3')

    the book that i have is on PDF and shows very little on what to do it just gives the theorems and example problems that have steps where they apply 4 theorems at once and an end result with no work shown. I'm not looking for simply answers (thought I'm guessing there are forum rules against it) but a detailed explanation of it would be wonderful.
     
  2. amishjeb

    New Member

    Sep 9, 2012
    14
    0
    This is probably a long shot, but are you in Majid's class at UCD?
     
  3. Maxoriley618

    Thread Starter New Member

    Sep 9, 2012
    13
    0
    Holy chirst yes, yes I am.
     
  4. amishjeb

    New Member

    Sep 9, 2012
    14
    0
    I would help if I could, but I only joined because I needed help too.
     
  5. Maxoriley618

    Thread Starter New Member

    Sep 9, 2012
    13
    0
    no problem hopefully we can get someone to help us here then!
     
  6. Maxoriley618

    Thread Starter New Member

    Sep 9, 2012
    13
    0
  7. Papabravo

    Expert

    Feb 24, 2006
    10,178
    1,799
    You can build a truth table.

    Each of the terms in the expression represents one or more lines in the truth table. Write a 1 in the output column for each term. If the two truth tables are the same the expressions are equivalent.

    LHS of the first expression
    X1'X3 --> 0x1 --> 001, 011
    X1X2X3 --> 111
    X1'X2 --> 01x --> 010, 011
    X1X2' --> 10x --> 100, 101

    The 1's in the truth table are on lines 1,2,3,4,5,7

    Code ( (Unknown Language)):
    1.  
    2. X1 X2 X3 | Y
    3. ---------------
    4. 0  0  0  | 0
    5. 0  0  1  | 1
    6. 0  1  0  | 1
    7. 0  1  1  | 1
    8. 1  0  0  | 1
    9. 1  0  1  | 1
    10. 1  1  0  | 0
    11. 1  1  1  | 1
    12.  
    Get the idea?
     
  8. MrChips

    Moderator

    Oct 2, 2009
    12,451
    3,371
    Nice. Your example is a lot clearer than my explanation.
    You're just a bit late joining in the party. I think they got it and went out for a beer.
     
  9. WBahn

    Moderator

    Mar 31, 2012
    17,788
    4,807
    The problems very likely expect solutions using Boolean algebraic manipulation. Using a truth table is a wonderful check (and it can also offer insight into the Boolean algebra that needs to be performed), but it may not be acceptable as the solution to the homework.

    On parts (b) and (c), I would recommend walking a truth table across for the expressions as given, then multiply out the expressions on each side to yield a sum of products for each side. It's not as bad as it might seem at first because lots of the products will be eliminated and or redundant. Then work with what's left.
     
Loading...