Boolean Algebra: Minimum SumOfProducts Expressionby Ithryndil Tags: algebra, boolean, expression, minimum, sumofproducts 

#1
Sep1309, 06:46 PM

P: 142

1. The problem statement, all variables and given/known data
Find the minimum SumOfProduct 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. 



#2
Sep1309, 10:51 PM

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, QuineMcCluskey). 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
Sep1309, 10:54 PM

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!




#4
Jul2910, 01:06 PM

P: 1

Boolean Algebra: Minimum SumOfProducts Expression
Karnaugh product of sums answer:
a(b+d)(b+c'+d') 


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