Okay so someone told me discrete maths would be easy...it is...kind of...but its very practical. And I'm not a very practical guy, I'm more of a algebra/calculus person. So I'm kind of struggling with 1004.
I just need help with the first question on the assignment sheet.
Consider the Boolean functions f(x, y, z) in three variables such that the table of values of f contains exactly four 1’s.
(i) Calculate the total number of such functions.
(ii) We apply the Karnaugh map method to such a function f. Suppose that the map does not contain any blocks of four 1’s, and all four 1’s are covered by three blocks of two 1’s. Moreover, we find that it is not possible to cover all 1’s by fewer than three blocks. Calculate the number
of the functions with this property.
for the first part, i got 8C4, since you cant have repetitions and its not asking for order?
but i dont understand the second part completely. in the karnaugh map, im thinking that one of the ways is to have like a Z shaped line of 1's?
like this:
1 1 0 0
0 1 1 0
i think this fits the requirements said in the question. but i dont understand the last sentence, how do calculate the number of functions with this property?
id be grateful if someone could help, thanks.
I just need help with the first question on the assignment sheet.
Consider the Boolean functions f(x, y, z) in three variables such that the table of values of f contains exactly four 1’s.
(i) Calculate the total number of such functions.
(ii) We apply the Karnaugh map method to such a function f. Suppose that the map does not contain any blocks of four 1’s, and all four 1’s are covered by three blocks of two 1’s. Moreover, we find that it is not possible to cover all 1’s by fewer than three blocks. Calculate the number
of the functions with this property.
for the first part, i got 8C4, since you cant have repetitions and its not asking for order?
but i dont understand the second part completely. in the karnaugh map, im thinking that one of the ways is to have like a Z shaped line of 1's?
like this:
1 1 0 0
0 1 1 0
i think this fits the requirements said in the question. but i dont understand the last sentence, how do calculate the number of functions with this property?
id be grateful if someone could help, thanks.
