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26 January, 21:22

I need to represent 2 million different numbers in binary. How many bits will I need to represent them in binary?

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Answers (1)
  1. 27 January, 00:19
    0
    21 bits

    Explanation:

    The formula that will be used is given as

    2^No. of bits = No. of combinations

    There we need to find

    No. of Bits?

    Given is

    No of Combinations = 2 million = 20,000,00

    so,

    2^ No. of bits = 20,000,00

    so

    No. of bits = Log 2 (20,000,00) = log 10 (20,000,00) / log 10 (2)

    = 20.93 which is approximately = 21

    So, 21 bits required for 2 million numbers.

    It means that, if we have 21 number of bits, we can make 2 million combinations.

    for example

    If we have 2 bits

    we can make

    2^2 combinations which is equal to 4.

    So four combinations with 2 bits are given below:

    0 00

    1 01

    2 10

    3 11
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