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•  » Converting boolean expression into disjunctive normal form

## #26 2013-08-14 20:12:05

dee93
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### Re: Converting boolean expression into disjunctive normal form

#### bob bundy wrote:

see diagram

Then decide which boxes to shade

Bob

2 on far right,and 1 on botton left same as post #17?

Last edited by dee93 (2013-08-14 20:45:30)

## #27 2013-08-14 23:12:19

bob bundy
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### Re: Converting boolean expression into disjunctive normal form

hi dee93

It cannot be the same as the other question because the logic statements are different.

Let's go back to first principles.

pq' means p is true and not q is true (or q is false)

A karnaugh map is a way of showing a logic expression diagrammatically.  It does a similar job to the venn diagrams I did earlier but copes better when the number of variables goes up.

In the boxes you can put expressions like pq'r or use 0 for false an d 1 for true (101 for this case) or express the logic in words: p true, q false, r true.  Below I've taken the earlier diagram and added more labels to show what each box means.

The problem you are trying to do is abc + ac

I would write that as (a AND b AND c) OR (a AND c)

abc is a single box as it represents the case where all three are true.

ac means that a AND c are both true but b can be either.  Because of this it will take two boxes.

But that does not mean that you will end up with three boxes shaded because one box is repeated.

Hope that helps.

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #28 2013-08-14 23:23:26

dee93
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### Re: Converting boolean expression into disjunctive normal form

#### bob bundy wrote:

hi dee93

It cannot be the same as the other question because the logic statements are different.

Let's go back to first principles.

pq' means p is true and not q is true (or q is false)

A karnaugh map is a way of showing a logic expression diagrammatically.  It does a similar job to the venn diagrams I did earlier but copes better when the number of variables goes up.

In the boxes you can put expressions like pq'r or use 0 for false an d 1 for true (101 for this case) or express the logic in words: p true, q false, r true.  Below I've taken the earlier diagram and added more labels to show what each box means.

The problem you are trying to do is abc + ac

I would write that as (a AND b AND c) OR (a AND c)

abc is a single box as it represents the case where all three are true.

ac means that a AND c are both true but b can be either.  Because of this it will take two boxes.

But that does not mean that you will end up with three boxes shaded because one box is repeated.

Hope that helps.

Bob

i've attempted to do it but unable to draw diagrams on here can you work it out so i can confirm mine is correct?

## #29 2013-08-15 02:12:57

bob bundy
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### Re: Converting boolean expression into disjunctive normal form

Compare with post 12

B

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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