boolean simplification

Discussion in 'Homework Help' started by fran1942, Apr 15, 2013.

Jul 26, 2010
58
0
Hello, I am trying to simplify the following:

AAB!C + ABB!C + ABC!C + AB!CD
(exclamation mark means NOT)

I keep on coming up with AB but I know the answer is AB!C

My working is as follows:

AAB!C + ABB!C + ABC!C + AB!CD
= AB!C + AB!C + AB + AB!CD
= AB!C + AB + AB!CD
= AB!C(D+1) + AB
= AB!C + AB
= AB(!C + 1)
= AB

Can anyone see where I am going wrong ?
Thanks kindly for any help.

2. MrChips Moderator

Oct 2, 2009
12,636
3,455
For starters,

BB! = 0
C!C = 0

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3. WBahn Moderator

Mar 31, 2012
18,087
4,917
The problem is in the simplification of your third term.

What does C!C reduce to?

Oh, and thank you very much for (1) posting your problem, (2) stating a specific question, and (3) showing your efforts at a solution. That is exactly the way it is supposed to work (and, sadly, so seldom the way it does work).

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4. MrChips Moderator

Oct 2, 2009
12,636
3,455
Sorry. I just realized your notation for NOT C is !C.

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5. WBahn Moderator

Mar 31, 2012
18,087
4,917
Ah, ya beat me!

I think, based on his last few lines, that he is using the ! as a prefix operator. Hence he would have

ABB!C = (A)(B)(B)(!C) = AB!C

I didn't say anything in my post, but this makes the point worth mentioning.

Using ! for logical inversion is ambiguous unless you include lot's of parenthesese, because some people use it as a prefix operator, !C, and others use it as a postfix operator, C!. I had to look for a spot in your work in which it could only be one or the other and, had there not been such a spot, would have been very confused by what you meant.

An alternative is to use the apostrophe for logical inversion. In theory, people could use it as either prefix or postfix, but I don't think I have ever seen it used as a prefix operator. Thus, in almost all cases,

ABBC' should be recognized as (A)(B)(B)(C')

though there are some who will misread it as (ABBC)'. But then !ABBC would likely be misread as !(ABBC) by those same people. The only bulletproof solution is to use lots of parens (or to provide an unabiguous key before your work).

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