# Boolean function implementation

Discussion in 'Homework Help' started by vvkannan, Nov 18, 2008.

1. ### vvkannan Thread Starter Active Member

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Aug 9, 2008
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I have some doubts regarding boolean function implementation using multiplexers.
If i have to implement a product of sum function like this
example:F(A,B,C,D)=pi M(0,3,5,7,8,9)+d(2,6)
and i convert this POS into SOP expression.should i have to remove all the dont cares?
Taking the above example should i write :sum m( 1,,4,10..15) or should i include the dont cares?
Cant we implement a boolean function directly from a POS expression?
Thank you

2. ### Ratch New Member

Joined:
Mar 20, 2007
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vvkannan,

I will try to eradicate those doubts. By the way, Boolean is capitalized because it is derived from a person's name. So is the personal pronoun "I" capitalized. And contractions use an apostrophe.

You include the don't cares because their terms can be present or missing in either the SOP or POS form of the equation.

Certainly, just use a AND gate instead of an OR gate.

Ratch

3. ### vvkannan Thread Starter Active Member

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Aug 9, 2008
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Thank you for correcting me.

So don't cares can either be included or not and it would not make any difference .
Thank you

4. ### Ratch New Member

Joined:
Mar 20, 2007
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vvkannan,

Oh, oh, I think you misunderstood me. I said that the terms that the don't cares represent could either be present or missing. Let me clarify. You use the don't cares if you need them to simplify a expression and discard them if you don't. It does make a difference if you don't use them if they can simplify a expression. In your example, PI M(0,3,5,7,8,9)+d(2,6), the complement is either SIGMA m(1,2,4,6,10-15) or SIGMA m(1,2,4,10-15) . The only difference between the two SIGMA expressions is the presence or absence of SIGMA m(2,6) . That is the definition of don't cares, so you can write the complement of PI M(0,3,5,7,8,9)+d(2,6) as SIGMA m(1,2,4,10-15)+d(2,6) . Another way to understand it better is to make a truth table and mark the don't cares with a "X". Then you can see that the don't care terms can be used for either the original expression or its complement.

Ratch

5. ### vvkannan Thread Starter Active Member

Joined:
Aug 9, 2008
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Thank you very much .Now you really have eradicated my doubts.