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!
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:
x x 1 0 x
1 1 x 0 0
x x x 1 1
0 1 x x 1
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!
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