Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am trying to figure out how to simply a canonical sum of products expression that is from this expression: $$ f_1(x_1,x_2,x_3) = \sum m (2,3,4,6,7) $$ where m is canonical minterms

I got: $$ \bar{x}_{1}x_2\bar{x}_3 + \bar{x}_{1}x_2x_3+x_1\bar{x}_{2}\bar{x}_{3}+x_1x_2\bar{x}_{3} + x_1x_2x_3 $$

then I simplify and get: $$ x_2+x_1x_2 $$

which is incorrect. I the answer in the book is: $$ x_2+x_1\bar{x}_{3} $$

share|cite|improve this question
What is $m$? And I think the word you want to use is "simplify", not "simply". – TMM Sep 22 '11 at 15:12
Sorry, I edited question for further clarity. – Nick Sep 22 '11 at 15:15
up vote 1 down vote accepted

Let $a = x_{1}$, $b = x_{2}$, and $c = x_{3}$.

Then to simplify $a'bc' + a'bc + ab'c' + abc' + abc$

$a'(bc' + bc) + a(b'c' + bc') + abc$

$a'(b(c' + c)) + a(c'(b' + b)) + abc$

$a'b + ac' + abc$

$a'b + a(c' + bc)$

$a'b + a(c' + b)$

$a'b + ac' + ab$

$b(a' + a) + ac'$

$b + ac'$

share|cite|improve this answer
genius! Thank you. I was doing fuzzy math, haha. – Nick Sep 22 '11 at 16:46

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.