# Boolean Algebra: Minimum Sum-Of-Products Expression

by Ithryndil
Tags: algebra, boolean, expression, minimum, sumofproducts
 P: 142 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.
 P: 286 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
 P: 142 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!
P: 1

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

Karnaugh product of sums answer:

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

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