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21 May, 07:32

How many bits would need to show on a binary odometer if you wanted to have the ability to count up to 500?

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  1. 21 May, 08:20
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    The binary system count 0 and before shifting left.

    Therefore repeated divisions of 500 by 2 will yield the bits as reminders.

    500/2 = 250 R 0

    250/2 = 125 R 0

    125/2 = 62 R 1

    62/2 = 31 R 0

    31/2 = 15 R 1

    15/2 = 7 R 1

    7/2 = 3 R 1

    3/2 = 1 R 1

    1/2 = 0 R 1

    Collect the remainders to defne the bnary digits.

    500 = 1 1 1 1 1 0 1 0 0

    We need 9 bits, defined by the bnary number that will show on a binary odometer.

    Answer: 1 1 1 1 1 0 1 0 0 (9 bits on an odometer)
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