How many bits will it take to represent the following sets of outcomes?
(For example, 1 bit is enough to represent male/female, and 2 bits to identify four seasons of spring, summer, fall, winter as of 22 = 4)
a. The uppercase alphabet A, B, . . . , Z
b. The digits 0, 1, . . . , 9
c. The seconds in a 24-hour day
d. The people in the United States (about 300,000,000 of them)
The minimal number of bits, n, that we need to represent a set with N members is the minimal number which satisfies:
N =< 2^n (N smaller or equal to 2^n)
so, taking the natural logarithm of both sides
ln (N) =< n*ln(2)
n >=ln(N)/ln(2) = ...
This solution determines how many bits it will take to represent different sets of outcomes.