# Find the number of unique minterms

Discussion in 'Homework Help' started by xEnOnn, Apr 22, 2011.

1. ### xEnOnn Thread Starter New Member

Feb 2, 2011
25
0
Say given a function like this one: $F(A,B,C,D,E) = C \cdot D' + A \cdot B \cdot D' \cdot E' + D \cdot E + A' \cdot B \cdot E$

Is there a quick way to find out the number of unique minterms?

I'm thinking like using some combinatorics method but couldn't figure out how I could do it. I plot out a little truth table like this:
 A B C D E x x 1 0 x 1 1 x 0 0 x x x 1 1 0 1 x x 1
where 'x' means there is a possibility of either A or A', B or B' and so on.

So I start counting this way: $2^{2} + 2^{1} + 2^{3} + 2 ^{2} = 18$. The number of "x" is the number in the power of 2.
Then from here, I could only know that there are LESS THAN 18 unique minterms in this function. But there are many repeated minterms in this total of 18, which I need to minus out to get the exact number of minterms. And I don't know how I could count the repeated number of minterms to minus from this total.

It is more of a question of permutation and combinatorics but I am thought if I could figure out how to do this, I could get the number of unique minterms a lot more faster than to list out the entire table.

Thanks for any help!

Last edited: Apr 22, 2011
2. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
I 'm not exactly sure of what you are trying to accomplish here. Is simplifying a boolean expression all you are trying to do? If so, your "truth table" doesn't help much.

First of all, it doesn't serve as one at all. It is more like a list of your given terms. The rows of a truth table are binarily numbered from 0 to 2^n-1, where n is the number of your variables.

I also don't understand where the counting you do is based on. Is the exponent the number of "x"s in each row or the fixed variables?

There is some theory on finding the solution with the smallest number of terms, but I don't think it can serve you right now in your level of understanding. I don't use it either. I think it is sufficient to read some theory, possibly here: http://www.allaboutcircuits.com/vol_4/chpt_8/index.html
and then do as many examples as you can.

Necessity is the best counselor here: The more you need the K-maps the better you will become at extracting them.