# Bits and Set Outcomes

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)

https://brainmass.com/engineering/electrical-engineering/bits-set-outcomes-223309

#### Solution Preview

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) = ...

#### Solution Summary

This solution determines how many bits it will take to represent different sets of outcomes.

$2.19