# Permutations question - 4k blocks

• Jul 21st 2009, 02:20 AM
dannyboy1121
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.
• Jul 21st 2009, 02:09 PM
awkward
Quote:

Originally Posted by dannyboy1121
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).
• Jul 24th 2009, 12:20 AM
dannyboy1121
Thanks
I just wanted to say thanks for taking the time to reply to this mail. It's much appreciated.