Advice required on Boolean algebra question

[Steve Collins]

I have been asked to simplify this Boolean expression:

~A~B~C~D + ~A~B~CD + ~A~BCD + ~AB~C~D + ~AB~CD + ~ABC~D + ~ABCD + A~B~C~D + A~B~CD

I have simplified it down to:

~AB + ~A~C + ~AD + ~C~B

But I know that the simplification goes further to:

~AB + ~AD + ~C~B

I've looked at the truth table and seen that ~A~C is indeed superfluous, but I am unsure of how to prove this algebraically.

 

[berkeman]

I have been asked to simplify this Boolean expression:

~A~B~C~D + ~A~B~CD + ~A~BCD + ~AB~C~D + ~AB~CD + ~ABC~D + ~ABCD + A~B~C~D + A~B~CD

I have simplified it down to:

~AB + ~A~C + ~AD + ~C~B

But I know that the simplification goes further to:

~AB + ~AD + ~C~B

I've looked at the truth table and seen that ~A~C is indeed superfluous, but I am unsure of how to prove this algebraically.

Can you use a Karnaugh map, or do you need to do it algebraically?

 

[Steve Collins]

It doesn't need to be done algebraically, I just thought that was the way to do it.
I've heard of a Karnaugh map before, but have no idea what it is or does. I will look it up now.

Cheers

Steve

 

[berkeman]

It doesn't need to be done algebraically, I just thought that was the way to do it.
I've heard of a Karnaugh map before, but have no idea what it is or does. I will look it up now.

Cheers

Steve

Great! Yeah, using a K-map I got the final 3 terms that you listed.

 

[Steve Collins]

Fantastic! I also found the 3 terms I was expecting and also solved another problem that was giving me some trouble.

Thanks berkeman.