# Canonical expression and truth table

1. Jun 2, 2013

### nelectrode

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. Jun 2, 2013

### Psinter

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.