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c. find the domain and range of the function that assigns to a bit string the number of ones minus the number of zeros in the string

Let bitstrings have a maximum length of L bits.

and f (x) = number of one-bits less number of zero-bits.

x=length of bitstring in bits.

Case 1: x=L, all L bits are ones

Then f (x) = L

Case 2: x=L, all L bits are zeroes

Then f (x) = - L

Then

dom f (x) = [0, L]

range f (x) = [-L, L]