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Canonical expression and truth table

  1. Jun 2, 2013 #1

    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.
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