Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Canonical expression and truth table

  1. Jun 2, 2013 #1
    Hey,

    What are the steps to follow to draw a truth table and create canonical expression
    from a given expression A?

    Lets say I have A= B'.(C'+D)


    1) first I have to draw the truth table for the expression above, but How could I do that since I only have one expression?


    2)Then I have to create canonical expression for this A=B'.(C'+D)
    ( but isnt that already in canonical?)
     
  2. jcsd
  3. Jun 2, 2013 #2
    That one is not really in canonical form. There are two canonical forms: SUM OF PRODUCTS and PRODUCT of SUMS. You can use boolean algebra to make it into any of the canonical forms, or you can use a truth table, or you can use a Karnaugh Map.

    A is the function here. So your variables are:
    B, C, and D.

    Since you have 3 variables your truth table will have 8 rows (2^3 = 8)

    It's like saying A(B,C,D) = B'.(C'+D) [A as a function of B, C, and D]

    You can make the truth table from there like this:
    ________________
    B | C | D | A(B, C, D)|
    0 | 0 | 0 | |
    0 | 0 | 1 | |
    0 | 1 | 0 | |
    0 | 1 | 1 | |
    1 | 0 | 0 | |
    1 | 0 | 1 | |
    1 | 1 | 0 | |
    1 | 1 | 1 | |
    --------------------------

    Now just fill the value of A. That is, plug in the values of B, C, and D to get A. Don't forget to negate those that are suppose to be negated in your A function (B and C in this case).

    2) To make the Canonical form of SUM OF PRODUCTS you just have to write down as product those BCD combinations that make A have a 1 and keep adding them. For example if the 000 make A(B,C,D) a 1 then you would have B'C'D'. Then if the 010 make the A(B,C,D) a 1 then you would have together with the last one: A = B'C'D' + B'CD'. And so on.

    If you want to have it in its simplest form use boolean algebra or a Karnaugh map which I recommend here.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Canonical expression and truth table
Loading...