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Simplifying equations using boolean algebra

  • Thread starter mrlupr
  • Start date
  • #1
4
0
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:

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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Welcome to PF!

Hi mrlupr! Welcome to PF! :smile:

Let's start with …
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:
 
  • #3
4
0
here is what I have so far.

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

how does it look?
 
  • #4
tiny-tim
Science Advisor
Homework Helper
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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:
 
  • #5
4
0
Ok how about this

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

am I any closer?
 
  • #6
tiny-tim
Science Advisor
Homework Helper
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249
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:
 
  • #7
4
0
Ok lets 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?
 
  • #8
tiny-tim
Science Advisor
Homework Helper
25,832
249
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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