0

I want to ask that if we are told to express an Boolean Expression in sum of min-terms which is already in non-standard SOP form. So do we need to express it in Standard SOP form or what?

For Example:

Express the following Boolean Function in sum of min-terms$$ F=ABC+BC+ACD$$

My Question:

Do we need to solve it like below?

$F=ABC+BC+ACD$

$F=ABC(D+D')+(A+A')BC(D+D')+A(B+B')CD$

$F=ABCD+ABCD'+ABCD+A'BCD+ABCD'+A'BCD'+ABCD+AB'CD$

Now using the OR Gate's Law, we would minimize it a little bit

$F=ABCD+ABCD'+A'BCD+A'BCD'+AB'CD$

Is this how we need to solve it? Or do we need to do it the other way, writing the Boolean Function in it's Binary Form and then convert those Binary numbers into decimals to get the min-terms and simply write them in Sigma notation to show sum of min-terms, like it has done in the following example?

enter image description here

Khubaib Khawar
  • 87
  • All literals must occur in the minterm exactly once (the range of literals is often implicit). The first formula for $f$ is SOP, but none of the terms is a minterm (the variables being $A,B,C,D$). – copper.hat Nov 12 '17 at 20:03
  • So what would be the method to express $F$ in the sum of min-terms? – Khubaib Khawar Nov 12 '17 at 20:05
  • The last formula you have for $F$ would work. Just expand and remove redundancies. – copper.hat Nov 12 '17 at 20:15
  • The one which is in the image? – Khubaib Khawar Nov 12 '17 at 20:18
  • 1
    I am saying you solved it correctly. The image is how you would map a product term onto minterms in a Karnaugh map. You can do it this was as well, but it is equivalent to the algebraic expansion that you already did. – copper.hat Nov 12 '17 at 20:22
  • what's the best approach in case of a long Boolean Expression like 5-var expression with 10 terms? Should I go for first formula or the second one? – Khubaib Khawar Nov 12 '17 at 20:36
  • 1
    They end up being the same, so whatever you prefer. In any case, the number of terms will explode quickly, so I wouldn't do it :-). – copper.hat Nov 12 '17 at 20:51
  • 1
    @copper.hat thanks a lot mate. I was confused that if I am doing correctly or not. :) – Khubaib Khawar Nov 12 '17 at 20:54

0 Answers0