# Simplifying equations using boolean algebra

• mrlupr
Ok how about thisabd+abd +bd+ abcd+bcd=a+abd+bd=bd+bdHow does it look?abd+abd +bd+ abcd+bcd=a+abd+bd=bd+bdf

#### mrlupr

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:
Welcome to PF!

Hi mrlupr! Welcome to PF!

Let's start with …
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?

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

Ok how about this

bcd+bcd
bd(c+c)
bd1

am I any closer?

Ok how about this

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 let's go

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

How does it look?

abd+abd +bd+ abcd+bcd
=a11+bd+ab`d

again … no idea what you're doing