# cant understand boolean algebra for the life of me!

Discussion in 'Homework Help' started by Maxoriley618, Sep 9, 2012.

1. ### Maxoriley618 Thread Starter New Member

Sep 9, 2012
13
0
Determine whether or not the following expressions are valid, i.e., whether the left- and
right-hand sides represent same function.
(a) x1'x3 + x1x2x3' + x1'x2 + x1x2' = x2'x3 + x1x3' + x2x3' + x1'x2x3
(b) x1x3' + x2x3 + x2'x3' = (x1 + x2' + x3)(x1 + x2 + x3')(x1' + x2 + x3')
(c) (x1 + x3)(x1' + x2' + x3')(x1' + x2) = (x1 + x2)(x2 + x3)(x1' + x3')

the book that i have is on PDF and shows very little on what to do it just gives the theorems and example problems that have steps where they apply 4 theorems at once and an end result with no work shown. I'm not looking for simply answers (thought I'm guessing there are forum rules against it) but a detailed explanation of it would be wonderful.

2. ### amishjeb New Member

Sep 9, 2012
14
0
This is probably a long shot, but are you in Majid's class at UCD?

3. ### Maxoriley618 Thread Starter New Member

Sep 9, 2012
13
0
Holy chirst yes, yes I am.

4. ### amishjeb New Member

Sep 9, 2012
14
0
I would help if I could, but I only joined because I needed help too.

5. ### Maxoriley618 Thread Starter New Member

Sep 9, 2012
13
0
no problem hopefully we can get someone to help us here then!

Sep 9, 2012
13
0
7. ### Papabravo Expert

Feb 24, 2006
10,340
1,850
You can build a truth table.

Each of the terms in the expression represents one or more lines in the truth table. Write a 1 in the output column for each term. If the two truth tables are the same the expressions are equivalent.

LHS of the first expression
X1'X3 --> 0x1 --> 001, 011
X1X2X3 --> 111
X1'X2 --> 01x --> 010, 011
X1X2' --> 10x --> 100, 101

The 1's in the truth table are on lines 1,2,3,4,5,7

Code ( (Unknown Language)):
1.
2. X1 X2 X3 | Y
3. ---------------
4. 0  0  0  | 0
5. 0  0  1  | 1
6. 0  1  0  | 1
7. 0  1  1  | 1
8. 1  0  0  | 1
9. 1  0  1  | 1
10. 1  1  0  | 0
11. 1  1  1  | 1
12.
Get the idea?

8. ### MrChips Moderator

Oct 2, 2009
12,633
3,453
Nice. Your example is a lot clearer than my explanation.
You're just a bit late joining in the party. I think they got it and went out for a beer.

9. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
The problems very likely expect solutions using Boolean algebraic manipulation. Using a truth table is a wonderful check (and it can also offer insight into the Boolean algebra that needs to be performed), but it may not be acceptable as the solution to the homework.

On parts (b) and (c), I would recommend walking a truth table across for the expressions as given, then multiply out the expressions on each side to yield a sum of products for each side. It's not as bad as it might seem at first because lots of the products will be eliminated and or redundant. Then work with what's left.