boolean algebra problem

[u24c02]

Hi.

I want to confirm the answer of this question's answer.

The boolean question is like this.
ab'+c

And my answer is ab'+c(a+b'+c);
But my book's answer is like this. ab'+c(a+b'+1);

What is the answer of the question? Am I do wrong?

 

[harpv]

Please explain how you arrived at your answer.

 

[u24c02]

ab'+c
=(a+c)(b'+c)
=ab'+ac+cb'+cc
=ab'+c(a+b'+c)

 

[dipin]

hi,

in boolean function x.x=x.
so c.c =c
regards

 

[u24c02]

Thanks, and
I'm trying to convert*SOP (Sum of Products) to POS (Product of Sums).

The question is like this.

ABC +AB'C'+AB'C+ABC'+A'B'C

I just want to know some technic how to convert SOP to POS? I got thus like this but I can't find any more.

ABC +AB'C'+AB'C+ABC'+A'B'C =A(BC+B'C'+B'C+BC')+A'B'C
=A(1+1)+A'B'C =A+A'B'C' ...

Would you please help me ? How to convert this?

 

[harpv]

@u24c02

For your first question :

There could also be something like this :

ab' + c
= ab' + c + ca + cb'  // from  a + ab = a
= ab' + c(a + b' + 1)

So basically the answer you are looking for isn't unique.

For the second question :

Apply DeMorgan's law :

F = ABC +AB'C'+AB'C+ABC'+A'B'C 

F' = A'B'C' + A'BC' + A'BC (the SOP of minterms not present in F)

F = (F')' = (A'B'C' + A'BC' + A'BC)'

I believe the rest you can work out yourself.

 

[dipin]

hi,

Thanks, and
I'm trying to convert*SOP (Sum of Products) to POS (Product of Sums).

The question is like this.

ABC +AB'C'+AB'C+ABC'+A'B'C

I just want to know some technic how to convert SOP to POS? I got thus like this but I can't find any more.

ABC +AB'C'+AB'C+ABC'+A'B'C =A(BC+B'C'+B'C+BC')+A'B'C
=A(1+1)+A'B'C

Would you please help me ? How to convert this?

After that apply the rule A+A'B = A+B

results
A+A'(B'C)=A+B'C

then apply the rule used in the #3 post

you will get (A+B')(A+C) which is in POS form.

regards

 

[u24c02]

@u24c02

For your first question :

There could also be something like this :

ab' + c
= ab' + c + ca + cb'  // from  a + ab = a
= ab' + c(a + b' + 1)

So basically the answer you are looking for isn't unique.

For the second question :

Apply DeMorgan's law :

F = ABC +AB'C'+AB'C+ABC'+A'B'C 

F' = A'B'C' + A'BC' + A'BC (the SOP of minterms not present in F)

F = (F')' = (A'B'C' + A'BC' + A'BC)'

I believe the rest you can work out yourself.

Thanks , How can you find minterm and maxterm?

 

[harpv]

I'm afraid you'll have to figure that out for yourself. Any basic digital electronics book should have the details you need.

If you can't find a book I'm sure a simple Google search will yield all the answers regarding boolean algebra.

 

[u24c02]

I get it
I will do that.