Can someone please explain why the F( X, Y ) is XY' + XY ? IMO , it is X'Y' + X'Y +XY' +XY .... or the author simplified it to become XY' + XY ? how to simplify it?
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Your four-term expression covers ALL four possibilities, and thus would reduce to F(X,Y)=True.Can someone please explain why the F( X, Y ) is XY' + XY ? IMO , it is X'Y' + X'Y +XY' +XY .... or the author simplified it to become XY' + XY ? how to simplify it?
no, can you explain further?Your four-term expression covers ALL four possibilities, and thus would reduce to F(X,Y)=True.
The expression XY' + XY reduces to just X. Do you see how that is the case?
Can you "factor out" the X from both terms?no, can you explain further?
And what is Y+Y' equal to?here's my working:
(X'Y') + (X'Y) + (XY') + (XY)
=XY +Y'(X' +X ) +X'Y
= XY +Y' +X'Y
=XY +Y' +X'Y
= Y(X +X') +Y'
= Y+Y'
X(Y+Y') +X'Y +X'Y'Can you "factor out" the X from both terms?
What does that leave you with?
What is (A+A') equal to?
Y+Y' = 1And what is Y+Y' equal to?
Where did you come up with that first expression? Remember that SOP is the sum of all the minterms for which the output is True. You can't just sum up all of the combinations because then you are saying that the output doesn't matter.
You are correct that F(X,Y) = XY' + XY does not agree with the table above it, though the table appears to extend to the right of the three columns you have shown, so it could be that there is something there that affects how the equation below it is supposed to be interpreted.in the attached file,
it is given that
"Here, the SOP is F(X,Y)=XY'+XY"
but I don't think that's true, because,
that equation doesn't satisfy for the values given in the truthtable
like,
X=0,Y=1,F=1
X.Y'+X.Y=(0.0)+(0.1)=0 but not 1
What about X=0, Y=0 or X=1, Y=1? Those are each supposed to yield F=0 but your expression yields F=1 for both (indeed, for ALL combinations).SOP would obviously be
X'Y'+XY'+X'Y+XY=1 (TRUE)
after reading your post, i have a several questions here:Okay, so where do these lead you?
Say we have four variables, {A,B,C,D}. If one of our terms is ABC, then this is NOT a minterm because it covers two combinations: It is true if {A,B,C,D} are all True, but is it also True if {A,B,C} are True but {D} is False. In order to be a minterm, it must have ALL four variables (with each variable being either complemented or noncomplemented).after reading your post, i have a several questions here:
1.) according to your notes , A minterm is a Boolean's expression that is true fir the minimum number of combinations of inputs ;this minimum number is exactly one. What do you mean by this? I still cant understand , can you please explain further ?
2.) A maxterm is a Boolean's expression that is true for the maximum number of combinations of inputs; this maximum number is exactly one fewer than the total number of possibilities . What do you mean by this? I still cant understand , can you please explain further ?
well , can you explain why the minterm involve multiplication operation , and why the maxterm involve addition operation?Say we have four variables, {A,B,C,D}. If one of our terms is ABC, then this is NOT a minterm because it covers two combinations: It is true if {A,B,C,D} are all True, but is it also True if {A,B,C} are True but {D} is False. In order to be a minterm, it must have ALL four variables (with each variable beinwellg either complemented or noncomplemented).
Similarly, A+B+C is False if {A,B,C,D} are all False, but it is also False if {A,B,C} are all False but {D} is True. In order to be a maxterm, it must have ALL four variables (with each variable being either complemented or noncomplemented).
Well, think about it (and it is described in the blog).well , can you explain why the minterm involve multiplication operation , and why the maxterm involve addition operation?
Direct application of the distributive property of OR over AND.@WBahn , how do you know to transform A' + B' +CC' into ( A' +B' +C)(A' +B' +C' ) ??
do you mean the F(X, Y) from the book is wrong? so the F(X, Y) should be X'Y'+XY'+X'Y+XY ?You are correct that F(X,Y) = XY' + XY does not agree with the table above it, though the table appears to extend to the right of the three columns you have shown, so it could be that there is something there that affects how the equation below it is supposed to be interpreted.
The issue of whether it should be X'Y'+XY'+X'Y+XY has already been addressed. This expression covers ALL FOUR possible combinations and is therefore ALWAYS true. Is the function represented by the truth table always true? If not, then you know that this expression is not the function for that truth table.do you mean the F(X, Y) from the book is wrong? so the F(X, Y) should be X'Y'+XY'+X'Y+XY ?