# Thread:

1. ## 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.

2. 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).

3. ## Thanks

I just wanted to say thanks for taking the time to reply to this mail. It's much appreciated.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9710613489151001, "perplexity_flag": "middle"}