# Simplifying equations using boolean algebra

I need to simplify these boolean expressions.

## Homework Statement

Problem A:
abd+abd+bcd+bcd+abcd+bcd

Problem B:
abcd+abd+abcd+abd+acd+abd+abcd

Problem C:
abcd+abcd+abd+abcd+bd+abd

## 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

tiny-tim
Homework Helper
Welcome to PF!

Hi mrlupr! Welcome to PF!

Problem A:
abd+abd+bcd+bcd+abcd+bcd

The bcd+bcdpart is easy …

what is that? …

and how much further can you get?

Hint: try grouping together all the terms with bd

here is what I have so far.

bcd+bcd
bbc+cdd
bc+cd
c+bd

how does it look?

tiny-tim
Homework Helper
here is what I have so far.

bcd+bcd
bbc+cdd
bc+cd
c+bd

how does it look?

sorry … i've no idea what you're doing

bcd+bcd
bd(c+c)
bd1

am I any closer?

tiny-tim
Homework Helper

bcd+bcd
bd(c+c)
bd1

am I any closer?

Yes, that's it!

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

bcd+bcd
= bd(c+c)
= bd

ok, now have a go at all the bd terms

Ok lets go

abd+abd +bd+ abcd+bcd
=a11+bd+abd
=a+abd+bd
=bd+bd

How does it look?

tiny-tim
abd+abd +bd+ abcd+bcd
=a11+bd+ab`d