Boolean function implementation

Thread Starter

vvkannan

Joined Aug 9, 2008
138
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
 

Ratch

Joined Mar 20, 2007
1,070
vvkannan,

I have some doubts regarding boolean function implementation using multiplexers
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.

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

Cant we implement a boolean function directly from a POS expression?
Certainly, just use a AND gate instead of an OR gate.

Ratch
 

Thread Starter

vvkannan

Joined Aug 9, 2008
138
Thank you for correcting me.




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

Ratch

Joined Mar 20, 2007
1,070
vvkannan,

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