Simplification of Boolean Expressions

[fazer2014]

Hi guys - I am really new here and am taking a very very elementary course in Logic circuits/Boolean algebra. We have been given a couple of simplification questions and I was convinced I had used all the theorems correctly but two of us got two different answers and we can't find who has gone wrong. Thankyou so much for your time.

1. Simplify the following Boolean Expression:

X = ((AB)'C(A' + (B+C)')'

Where ' indicates NOT.

Homework Equations

De Morgan, very basic boolean operation rules.

The Attempt at a Solution

It's much much easier to read because both solutions (we can't decide which one is correct) have been typed up - so I AM going to post images. But please don't think it's out of laziness - I legitimately think it's much easier to read! We have been trying to figure out who is correct for hours (if either of us are correct at all)...

 

[CompuChip]

One thing you could try is making the truth tables for both results.

 

[NascentOxygen]

Hi nicola_a,

The two answers are not different.


AB + ^┓C + AC

= ^┓C + A(B+C)

For this,
if C=0, then this evaluates as true
if C=1, then (B+C) evaluates as true, so OR'ing with B is superfluous

= ^┓C + AC

Now,
if C=0, this evaluates as true
if C=1 ...

I leave you to justify dropping the AND'ing with C here.

 

[fazer2014]

Thankyou CompuChip, I realized by drawing the truth table that they are they same!
And as I was drawing the truth table, you replied Nascent, so thank you too!
I didn't think of doing that - VERY new at this (only a few lectures into the course).
Thank you so much :) It was driving me nuts!