Register to reply

Boolean Algebra: Minimum Sum-Of-Products Expression

Share this thread:
Sep13-09, 06:46 PM
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.
Phys.Org News Partner Science news on
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker
Sep13-09, 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, 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.

Sep13-09, 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!

Jul29-10, 01:06 PM
P: 1
Boolean Algebra: Minimum Sum-Of-Products Expression

Karnaugh product of sums answer:


Register to reply

Related Discussions
Finding an expression for the minimum drag coefficient Engineering, Comp Sci, & Technology Homework 7
Boolean Expression Proofs Engineering, Comp Sci, & Technology Homework 0
Reduce boolean expression to 3 literals Engineering, Comp Sci, & Technology Homework 8
What is a 'minimum NAND expression' Electrical Engineering 2