• Support PF! Buy your school textbooks, materials and every day products Here!

Simplify the boolean expression

  • Thread starter larry21
  • Start date
  • #1
10
0

Homework Statement


Build the truth tables for the boolean expressions.

(x + y' * z)' + (x * y * z' + (y + z)') + (y + (x * z')')'

The Attempt at a Solution


Given that the expression is so complex I believe that I need to simplify first then proceed to build the truth table?

Work so far:
(x + y' * z)' + (x * y * z' + (y + z)') + (y + (x * z')')'

1.) x' * y'' + z' + (x * y * z' + y' + z') + y' * (x * z')''
2.) x' * y + z' + (x * y * z' + y' + z') + y' * x * z'

Steps:
1. De Morgan
2. De Morgan and double negation

Kind of stuck at this point....
Help would be appreciated. Thanks in advance.
 

Answers and Replies

  • #2
collinsmark
Homework Helper
Gold Member
2,894
1,232
If it were me, I'd skip the simplification and go straight to the truth table. There's only three input variables (x, y and z), so your truth table has only eight rows.

There's nothing stopping you from simplifying beforehand, but as it turns out, going straight to the truth table is often the easiest approach.

The reason I say this is because the usual approach to minimization is:
(1) Build the truth table
(2) Use the truth table to make a Karnaugh map (K-map) and simplify that way (or use the Quine–McCluskey algorithm or equivalent).

Simplifying before the truth table sort of defeats the point. Sure, you can do it, but it might not be the best way to expend your effort.
 
Last edited:
  • Like
Likes 1 person
  • #3
collinsmark
Homework Helper
Gold Member
2,894
1,232
That said,

If you do choose to simplify a little before making the truth table, I suggest trying to put the expression in the form of "Sum of Products." It makes it a little easier to fill in the table that way. It's not totally necessary, but it couldn't hurt.

There are a couple of mistakes below I think.

Work so far:
(x + y' * z)' + (x * y * z' + (y + z)') + (y + (x * z')')'

1.) x' * y'' + z' + (x * y * z' + y' + z') + y' * (x * z')''
2.) x' * y + z' + (x * y * z' + y' + z') + y' * x * z'
I think you mean, (changes in red)

1.) x' * (y'' + z') + (x * y * z' + y' * z') + y' * (x * z')''
2.) x' * (y + z') + (x * y * z' + y' * z') + y' * x * z'
 

Related Threads on Simplify the boolean expression

  • Last Post
Replies
1
Views
311
  • Last Post
Replies
3
Views
495
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
7K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
13
Views
2K
Replies
1
Views
623
Top