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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) ?

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Answers (1)
  1. 2 July, 09:37
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    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.
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