# Boolean Identities

Discussion in 'Homework Help' started by JasonL, Dec 3, 2012.

1. ### JasonL Thread Starter Active Member

Jul 1, 2011
47
0
How do I simply AB + BC + AC' + BCD using boolean identities?
Using a K-map I know the answer is AC' + BC.

This is what I did so far
AB + BC + AC' + BCD
AB + AC' + BC(1+D)
AB + AC' + BC
I don't know how to simplify using identities beyond this point.

2. ### WBahn Moderator

Mar 31, 2012
23,587
7,215
Q1) Given what you've got so far, which of the three terms needs to be made to disappear?

Q2) Can you start from the other two terms (i.e., the answer) and figure out how to produce the third term? Sometimes this is much easier to do. If so, then to that carefully and then just reverse the steps to go the other way.

Hint: How can you take f(X,Y,Z) = XY and turn it into two terms each of which involved X, Y, and Z (or, of course, their complement)?

3. ### JasonL Thread Starter Active Member

Jul 1, 2011
47
0
Thanks! I expanded AB
AB + BC + AC'
ABC + ABC' + BC + AC'
BC(A+1) + ABC' + AC'
BC + AC'(B+1)
BC + AC'

4. ### WBahn Moderator

Mar 31, 2012
23,587
7,215
Great.

In doing your write up, include the step

AB + BC + AC'
AB(C+C') + BC + AC' <----
ABC + ABC' + BC + AC'

So that your reasoning is obvious.