Question

Can someone help me find the 16 Boolean function combinations? so i have:

xy + xy
xy + xy’
xy + x’y
xy’ + xy

x’y + xy
x’y + xy’
x’y + x’y
xy’ + xy’

xy’ + x’y
xy + x’y’
x’y’ + xy
x’y + x’y’

xy’ + x’y’
x’y’+ xy’
x’y’ + x’y
x’y’ + x’y’

and if there are no repeats then i only have 13:

Singles:
xy
xy’
x’y
x’y’

same:
xy + xy
x’y + x’y
xy’ + xy’
x’y’ + x’y’

double:
xy + x’y’

single:
xy + xy’
xy + x’y

triple:
xy’ + x’y’
x’y + x’y’

Answer 1

@misty1212 if you know anything about discrete math and boolean functions i could really use some help with putting the 16 boolean functions into sum of product form

Answer 2

it is asking me to:Using the variables x and y, list all the Boolean functions on two variables. Be sure to give them in sum-of-products form.

Answer 3

Well it might help if you know what it is you're specifically looking for rather than trying to just shotgun every possibility out there and hope you get it. Do you know what you're specifically missing or should I explain how to figure that out?

Answer 4

please explain have been at this for hours and the text book they provided us doesn't even cover anything about sum of products...

Answer 5

i know that there are a total of 16 boolean functions on 2 variables, i and having trouble finding them all and putting them in sop

Answer 6

Well there are 16 different outputs because there are \(2^4\) ways you can get a single function to take you from the 4 cases (T,T), (T,F), (F,T), (FF) to trues and false since each can be either T or F, so each of the 2 cases 4 times is all 16, kind of weird.

I haven't really done this sort of thing in a while, so I'm not sure I'll be able to help you very much sorry.

Answer 7

do you know how sum of products work?

Answer 8

I believe it's mod 2 arithmetic, but I'm not sure. That might help give a word for you to search for though. Modular arithmetic.