# Quick simplification check

Discussion in 'Homework Help' started by Gotmilk0112, Apr 21, 2013.

1. ### Gotmilk0112 Thread Starter Member

Mar 24, 2013
32
0
Need a quick simplification check for simplifying boolean variables into XOR statements.

P1, P2, P3, P4, B are just normal variables, in this case of simplification.

Ja = P1P2'P3'P4'B' + P1'P2P3'P4'1 + P1'P2'P3P4'B' + P1'P2'P3'P4B'
= (P1 xor P3 xor P4)  B' + P1'P2P3'P4'1

Ka = P1P2'P3'P4'1 + P1'P2P3'P4'B' + P1'P2'P3P4'1 + P1'P2'P3'P4B'
= (P2 xor P4)  B' + (P1 xor P3)  1

Is this correct? I'm not sure exactly how to simplify into XOR statements with so many variables like this.

2. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
The beautiful thing about manipulating logic expressions is that you can always verify whether or not they match by generating the truth tables for both sides and seeing if they agree.

Do they?

Before doing the full up table, do some sanity checks. For instance, for Ka, what will your simplified expression result in for the case of B=1, P1=1, P2=1, P3=0, P4=0 ? What should Ka be for this set of inputs?

3. ### Gotmilk0112 Thread Starter Member

Mar 24, 2013
32
0
Uh...I don't know what Ka would be for that set of inputs. I don't even know where to start, there.

4. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
Let's take it one step at a time.

For that set of inputs, would (P2 xor P4) be a 0 or a 1?

5. ### Gotmilk0112 Thread Starter Member

Mar 24, 2013
32
0
(1 xor 0) = 1

6. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
Good.

Now will B' be a 0 or a 1?

Mar 24, 2013
32
0
1' = 0

8. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
Good.

You said, "I don't know what Ka would be for that set of inputs. I don't even know where to start, there." I am just taking you at your word and walking you through it step by step. I'm hoping that, at some point, something will click and you will grab the ball and run with it.

Now, is (P2 xor P4) * B' a 0 or a 1?

Mar 24, 2013
32
0
1 * 0 = 0

10char

10. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
I don't know if "10char" was supposed to mean anything or is just orphaned text that didn't get deleted.

So fine. Now let's move to the second term.

Will (P1 xor P3) be a 0 or a 1?

11. ### Gotmilk0112 Thread Starter Member

Mar 24, 2013
32
0
1 xor 0 = 1

I still don't see where this is going.

12. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
Good.

Now, will (P1 xor P3) * 1 be 0 or 1?

The fact that you don't see where this is going when the goal has been clearly stated that we are trying to find out what Ka is for a particular set of inputs for both the original expression and your proposed simplification of it is quite troubling. But, perhaps something will still click.

13. ### Gotmilk0112 Thread Starter Member

Mar 24, 2013
32
0
I don't see how this is helping me simplify the sets of variables.

But if you insist...

1 * 1 = 1

14. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
Good, so now, is

Ka = (P2 xor P4) • B' + (P1 xor P3) • 1

a 0 or a 1 for this set of inputs?

15. ### Gotmilk0112 Thread Starter Member

Mar 24, 2013
32
0
1 * 0 + 1 * 1 = 1

I seriously don't see how this is helping. Can we just get to the point already?

Mar 31, 2012
18,087
4,917