Boolean Help: Solving Your Problem with Ease

[krispiekr3am]

Can someone help me with this problem.

 

[krispiekr3am]

i wanted to proof that that boolean is true. thank you

i wanted to proof that that boolean is true. thank you

 

[krispiekr3am]

I need to simplify the following expressions in XOR The simplified answer is only one variable or its complement

 

[CRGreathouse]

I can't see the JPEG yet. Why don't you explain the problem and what you've done so far?

 

[0rthodontist]

You could use the definition of XOR in terms of and and or. Or you could work directly in terms of XOR. Some properties of XOR can be found here:
http://en.wikipedia.org/wiki/XOR#Properties

 

[haki]

One alternative - you can generate a truth table of the expression and see from the table what it is done, but I doubt that any Math teacher would like that, anyway

For example a
I believe that you can rearrange the terms and you can simplify them

e.g.

A'B XOR BC XOR AB XOR B'C'

becomes

A'B XOR AB XOR BC XOR B'C'

note:
A'B XOR AB - what does that tell you?

you can simplyfiy this to get just one variable

then take BC XOR B'C'

how can you get a more simple equivalent of this of a form Y XOR Z where Y and Z represent one variable e.g. B or C'.

When you have this done you should see the answer.

Example b is a tautology.

 

[krispiekr3am]

A'b Xor Ab = B?

 

[krispiekr3am]

Bc Xor B'c'
=(b Xor C)'
=b+c'
=b' Xor C = Bc + B'c'
= B=c?

So The Answer Would Be B Xor (b = C) = 0??

 

[krispiekr3am]

B Xor (b Ξ C)

 

[krispiekr3am]

TO approve this other problem
AB XOR A'B XOR A'B' XOR B'A
B(A XOR A') XOR B'(A' XOR A)

we know that A XOR A' =1

B XOR B'

and from one of the XOR property, X XOR X' = 1
THEREFORE B EQUALY 1?
THE SOLUTION WOULD BE 1?
let me know if that right?

 

[krispiekr3am]

i think i did the 1st problem wrong...
here is the simplied solution
A'B xor BC xor AB xor B'C'
becomes
A'B xor AB xor BC xor B'C'

A'B xor AB = B (we know that A A' =1)

BC xor B'C'
= (B xor C')(C xor B')

B xor (B xor C')(C xor B')

 

[haki]

A'B xor BC xor AB xor B'C'

this is just one possibility:

step 1. - rearrange (correct)

A'B xor AB xor BC xor B'C'

step 2 - A'B xor AB is equivalent to just using B (correct), we have now

B xor BC xor B'C'

step 3 - BC xor B'C' is equivalent to B xor C' we are allowed to do this, since substituiting this will not alter the value of the overall truth table

B xor B xor C'

step 4 - B xor B will always be 0 we have now

0 xor C'

step 5 - 0 xor C' depends only on the value of C'

result: C'

this is ofcorse just one possibility.

you got the B example right.

A'B xor AB = B (we know that A A' =1)
what has A A' got to do with it?

 

[krispiekr3am]

Thank You So Much. That Really Helped.
Thanks Everyone