Question

How many bits are necessary for a binary representation (unsigned) of:

a. The states of the U.S.A.?

b. The days in a year?

c. The inhabitants of California (est. 36,457,549)?

Answer 1

Hi!

The answer to:

a. 6 bits.

b. 9 bits.

c. 26 bits.

Explanation:

a. For the states of the U.S.A, you need 50 or more combinations to represents each element.

If you use 6 bits, the possible combinations are 2⁶ = 64.

b. For days in a year, you need 365 or more combinations to represents each element.

If you use 9 bits, the possible combinations are 2⁹ = 512.

c. For inhabitants of California, you need 36,457,549 or more combinations to represents each element.

If you use 26 bits, the possible combinations are 2²⁶ = 67,108,864. If you use 25 bits instead of 26, then you have 2²⁵ = 33,554,432 combinations. These possible combinations are not enough to represent each inhabitant.