Books will tend to do that. For several reasons. The author may have messed up -- perhaps they changed the problem but not the solution, perhaps they just had a brain fart, perhaps they just made a silly typo. The editor/publisher may have screwed up. The grad student that they paid slave wages to to work all the problems and prepare the solutions manual may have screwed up. Whenever you don't agree with a provided answer, take it as an opportunity to solve a real problem, namely whose solution is actually correct. Don't blindly assume that the book is right, but don't assume that it is wrong too quickly, either. When there is disagreement, the goal is to PROVE which one is wrong (and perhaps both are) and be able to defend your conclusions -- you will learn a LOT in the process.

hi , i have one more example here involving 3 variables , X , Y , Z . i am having problem with the SOP and POS here.
i. ) for the SOP , why the X , Y AND Z can be false at the same time? As you can see it , the SOR contains X'Y'Z'
ii. ) For the POS , why it contain XYZ ? didn't you say that XYZ can be true at the same time?

 

hi , i have one more example here involving 3 variables , X , Y , Z . i am having problem with the SOP and POS here.
i. ) for the SOP , why the X , Y AND Z can be false at the same time? As you can see it , the SOR contains X'Y'Z'
ii. ) For the POS , why it contain XYZ ? didn't you say that XYZ can be true at the same time?

You should start a new thread with a new problem. Otherwise you will get responses to each all mixed together and it will become chaos. I'll report your post to the mod team who will split off the new problem into a new thread, so don't worry about it.

Look at your truth table.

If X is False, Y is False, and Z is False, then you want F to be True. So that means that the minterm that covers that combination needs to be included in the SOP equation. Remember, in the standard SOP form, there is exactly one minterm for each combination of inputs that should yield a True output, all of which are ORed together.

Similarly, in the standard POS form, there is exactly one maxterm for each combination of inputs that should yield a False output, all of which are ANDed together.

I don't understand your second question. Of course X, Y, and Z can be true at the same time. But that has no bearing on whether the output of the function should be True of False for that combination -- that is defined by the truth table for the function.

Now, for that second problem, count up how many minterms there are in their SOP expression. Does this match the number of rows for which the function is supposed to be True? If not, which one(s) do(es)n't match? Ask a similar question for the POS expression?

Are you sure that the expressions below the table are for the function defined by the table? If that's the case, you might consider getting a different book. While all books have errors, there comes a point where the errors are too extensive to continue bothering with.

 

Look at your truth table.

If X is False, Y is False, and Z is False, then you want F to be True. So that means that the minterm that covers that combination needs to be included in the SOP equation. Remember, in the standard SOP form, there is exactly one minterm for each combination of inputs that should yield a True output, all of which are ORed together.

why the book is giving F(X , Y, Z ) = X'Y'Z' +X'YZ +XY'Z +XYZ'
Shouldn't be the F(X,Y,Z ) be any one of the 8 possible outcomes(minterm) ?

 

Hello,

Please start a new threda when you have an other question.
For now I moved these post from this thread:
Boolean's Algebra - SOP

Bertus

 

hi , i have one more example here involving 3 variables , X , Y , Z . i am having problem with the SOP and POS here.
i. ) for the SOP , why the X , Y AND Z can be false at the same time? As you can see it , the SOR contains X'Y'Z'
ii. ) For the POS , why it contain XYZ ? didn't you say that XYZ can be true at the same time?

You need a new book! The posed problem shows a truth table with three 'true' results and the answer has four of them summed.

The inputs X,Y and Z can be false at the same time: they can have any of eight possible values.
A truth-table specifies the output for every one of those eight values. Only some of those outputs are 'true': those values are included in the equation.

 

You need a new book! The posed problem shows a truth table with three 'true' results and the answer has four of them summed.

The inputs X,Y and Z can be false at the same time: they can have any of eight possible values.
A truth-table specifies the output for every one of those eight values. Only some of those outputs are 'true': those values are included in the equation.

So can you please tell me what should the F(X, Y) for the above question?

 

So can you please tell me what should the F(X, Y) for the above question?

You should be able to take a pretty good shot at it by now.

Identify the rows in the truth table for which the output of the function should be True.

OR together the minterms for those rows (and only those rows).