# Homework Help: Boolean Algebra: Minimum Sum-Of-Products Expression

1. Sep 13, 2009

### Ithryndil

1. The problem statement, all variables and given/known data

Find the minimum Sum-Of-Product Expression for:
f = ab'c' + abd + ab'cd'

3. The attempt at a solution

By introducing the missing variable in term 1 and term 2 I can get an expression that has all the variables: a, b, c, and d.

I do so by:

f = ab'c'd + ab'c'd' + abcd + abc'd + ab'cd'

I can combine terms like so: (1 & 2),( 2 & 5), (3 & 4) I get:

f = ab'c' + ab'd' + abd

This hardly seems minimized from the original expression. Thanks for any help.

Last edited: Sep 13, 2009
2. Sep 13, 2009

### Elucidus

What you've stated is one of two equivalent minsum forms of that Boolean expression. There are several methods for arriving at these (consensus, Karaugh maps, Quine-McCluskey). I'd examine them for more info.

The original expression has a summand complexity (SC) of 3 and a literal complexity (LC) of 10. The minsum has an SC of 3 and an LC of 9 (as does the other). It isn't much simpler but it as simple as one can get.

--Elucidus

3. Sep 13, 2009

### Ithryndil

Thanks, when you're learning about these concepts it is nice to have confirmation that you are doing things right. Normally it class we get the function down a term or two...or even to one term. So, when I got this down to three terms, with three variables in each term, it didn't really seem minimized. Thanks again!

4. Jul 29, 2010

### touchpoint

Karnaugh product of sums answer:

a(b+d)(b+c'+d')

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook