Digital logic - Boolean algebra simplification problem

  • Thread starter theBEAST
  • Start date
  • #1
366
0

Homework Statement


Simplify (A+B')(B+C)

The Attempt at a Solution


I first expanded it and got
= AB + AC + B'B + B'C
= AB + AC + B'C

Turns out the solution is AB + B'C (according to an online source). How do we get rid of the AC term?
 

Answers and Replies

  • #2
NascentOxygen
Staff Emeritus
Science Advisor
9,244
1,072
On examining the expression, you can see ....
If B is true, then for the expression to be true, the only condition that need be met is that A is true, and it doesn't matter what C is.

If B is false, then for the expression to be true all we need is that C is true, it doesn't matter what A is.

Just as in algebra you can multiply any term by 1 and you don't change its value, then in Boolean algebra you can multiply a term by true and you change nothing.

For example, (B+B') is true, and it's always true.

AB + AC(B+B') + B'C

expand this out, then simpify the result
 

Related Threads on Digital logic - Boolean algebra simplification problem

Replies
5
Views
630
  • Last Post
Replies
1
Views
584
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
5
Views
2K
Replies
3
Views
517
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
0
Views
1K
Replies
0
Views
3K
Top