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Math Help - Permutations question - 4k blocks

  1. #1
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    Permutations question - 4k blocks

    Hi Folks,

    I'm not a student - but investigating the theoretical side of my work appears to have lead me to mathematics.

    So, I have a question and I hope I'm in the right section . I'm happy to receive a straight answer but would also like to learn how the answer was derived so I can do it myself in future.

    It's to do with how data is stored on a disk:

    Storage is held in the following units (ascending order)
    Bits - Bytes - Kilobytes (or k)

    Let's say that each block of data held on the disk is 4k in size - that means for arguments sake that there are 4000 bytes per 4k block.

    Each byte is made up of 8 bits. The bits are boolean.

    Now - I'm advised that there are 256 combinations of 1 and 0 in an 8 bit byte. If there are 4000 of them in a 4k block, how many permutations of 4k block are there?

    Any help appreciated.
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  2. #2
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    Quote Originally Posted by dannyboy1121 View Post
    Hi Folks,

    I'm not a student - but investigating the theoretical side of my work appears to have lead me to mathematics.

    So, I have a question and I hope I'm in the right section . I'm happy to receive a straight answer but would also like to learn how the answer was derived so I can do it myself in future.

    It's to do with how data is stored on a disk:

    Storage is held in the following units (ascending order)
    Bits - Bytes - Kilobytes (or k)

    Let's say that each block of data held on the disk is 4k in size - that means for arguments sake that there are 4000 bytes per 4k block.

    Each byte is made up of 8 bits. The bits are boolean.

    Now - I'm advised that there are 256 combinations of 1 and 0 in an 8 bit byte. If there are 4000 of them in a 4k block, how many permutations of 4k block are there?

    Any help appreciated.
    If I may rephrase your question, I think you are asking how many 4,000-byte blocks are possible if each byte is 8 bits. The answer is

    2^(8 * 4,000) = 2^32,000

    which is approximately 9.117 \times 10^{9632}

    (a pretty big number).
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  3. #3
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    Thanks

    I just wanted to say thanks for taking the time to reply to this mail. It's much appreciated.
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