help with boolean expressions and truth table

Discussion in 'Homework Help' started by fishguts, Oct 23, 2007.

  1. fishguts

    Thread Starter Member

    Sep 3, 2007
    22
    0
    I need to make a truth table for the following equation, but I have no idea where to start I have not seen an equation like this before

    F=(A+!B+C)(A+!C)(B+!C)

    I was also wondering if I simplified this equation correctly

    F=AB!C!D+ABC!D+!AD+AD = AB!D+ D
     
  2. thingmaker3

    Retired Moderator

    May 16, 2005
    5,072
    6
    To create your truth table, make one column for A, one for B, one for C, and one for F.

    Fill in the first three columns with the eight possible combinations. Apply the equation to each row to determine if F is true or false for that row. Tedious, yes, but not difficult.:)
     
  3. fishguts

    Thread Starter Member

    Sep 3, 2007
    22
    0
    Alright so for

    F=(A+!B+C)(A+!C)(B+!C)

    I just make a truth table liek any other equation? There is not anything special to do since it contains ()?
     
  4. Papabravo

    Expert

    Feb 24, 2006
    10,170
    1,797
    You do know that the three expressions in parentheses are to be AND'ed together -- don't you? In the algebra of real numbers the implied operation would be multiplication.
     
  5. thingmaker3

    Retired Moderator

    May 16, 2005
    5,072
    6
    No matter how the equation is re-phrased, there are still only three variables. That means three input columns in the table. All truth tables work the same way. :)

    Doing the algebra first would, of course, make table generation easier.
     
  6. techroomt

    Senior Member

    May 19, 2004
    198
    1
    if you convert your maxterm equation to a minterm, truth table generation is much simpler.
     
  7. Karandeep Singh

    New Member

    Oct 30, 2007
    6
    0
    iam not sure

    but method to decode can be by using de morgan theorem
    (A+!B+C)(A+!C)(B+!C)
    BY DE MORGAN
    AND SOLVING I GET
    B(A.{C BAR}+C)
     
  8. agentofdarkness

    Active Member

    Oct 9, 2007
    42
    0
    What does !Variable mean?
     
  9. Papabravo

    Expert

    Feb 24, 2006
    10,170
    1,797
    Exclamation point "!" is a commonly use symbol for "NOT" or "Complement"

    So if A=0 then !A=1 and vice versa
     
  10. agentofdarkness

    Active Member

    Oct 9, 2007
    42
    0
    I think the easiest way to generate a truth table is to first write down all the combinations of A,B,C (000-111). Then fill in the maxterms. A max term is combination of variables that will give you a result of logic 0. For this equation, 2 (ABC=010) is a maxterm. For all the blank spaces you get after you fill in the maxterms, fill in 1s. The maxterms will be
    2(010)
    1(001)
    3(011)
    1(001)
    5(101)

    Fill all the other rows with 1s. This form is known as Product of Sums. You have probably already solved the problem but hopefully some other people will find it helpful. I know that when I was first learning this stuff I had problems with it as well.
     
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