Simplifying equations using boolean algebra

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Homework Help Overview

The discussion revolves around simplifying boolean expressions, specifically three problems involving combinations of AND, OR, and NOT operations. Participants are attempting to apply boolean algebra rules to achieve simplification.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are sharing their attempts at simplifying the expressions, questioning the correctness of their steps, and seeking clarification on specific parts of the simplification process. There is a focus on grouping terms and applying boolean identities.

Discussion Status

The discussion is active, with participants providing hints and feedback on each other's attempts. Some guidance has been offered regarding grouping terms, and there is an ongoing exploration of different approaches to simplify the expressions.

Contextual Notes

Participants express uncertainty about their progress and the correctness of their methods, indicating a lack of confidence in their understanding of the boolean algebra rules being applied.

mrlupr
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I need to simplify these boolean expressions.

Homework Statement



Problem A:
a`b`d+a`bd`+bc`d`+bcd`+ab`c`d+b`cd

Problem B:
a`b`cd+a`bd+abcd+a`b`d+acd+abd+ab`c`d

Problem C:
a`b`c`d`+a`b`cd`+a`bd+ab`c`d`+bd+ab`d`

Homework Equations



abc means a AND b AND c
a+b means a OR b
a` means NOT a

The Attempt at a Solution



I have been working on these for over 6 hours and I still have a mess. I look at the rules and try to apply them, but I know my answers are incorrect.
 
Last edited:
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Welcome to PF!

Hi mrlupr! Welcome to PF! :smile:

Let's start with …
mrlupr said:
Problem A:
a`b`d+a`bd`+bc`d`+bcd`+ab`c`d+b`cd

The bc`d`+bcd`part is easy …

what is that? …

and how much further can you get?

Hint: try grouping together all the terms with b`d :wink:
 
here is what I have so far.

bc`d`+bcd`
bbc`+cd`d`
bc`+c`d
c`+bd

how does it look?
 
mrlupr said:
here is what I have so far.

bc`d`+bcd`
bbc`+cd`d`
bc`+c`d
c`+bd

how does it look?

sorry … I've no idea what you're doing :confused:
 
Ok how about this

bc`d`+bcd`
bd`(c`+c)
bd`1

am I any closer?
 
mrlupr said:
Ok how about this

bc`d`+bcd`
bd`(c`+c)
bd`1

am I any closer?

Yes, that's it!

But write it with = signs, and there's no need to write 1 …

bc`d`+bcd`
= bd`(c`+c)
= bd` :smile:

ok, now have a go at all the b`d terms :wink:​
 
Ok let's go

a`b`d+a`bd` +bd`+ ab`c`d+b`cd`
=a`11+bd`+ab`d
=a`+ab`d+bd`
=b`d+bd`

How does it look?
 
mrlupr said:
a`b`d+a`bd` +bd`+ ab`c`d+b`cd`
=a`11+bd`+ab`d

again … no idea what you're doing :confused:
 

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