Map a Byte Offset to a Block Number

Topic Overview

Bytes Map to Fixed Blocks

Disks and SSDs expose storage in sectors or pages, often 4096 bytes. Database engines map a byte offset to (offset / block_size) to find the containing block. SQLite, PostgreSQL, and MySQL buffer managers all start with this arithmetic before reading a page from disk.

Block Number Math

Integer division truncates toward zero for non-negative offsets. The remainder tells you where inside the block the byte lives.

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• Page 0 usually holds file headers in embedded databases
• Alignment requirements mean small writes may still touch whole blocks
• Use 64-bit offsets for multi-terabyte files
• This mapping is pure math; no filesystem calls required in the exercise

Working Through the Exercise

Keep the relevant documentation open while you implement. When your output disagrees with the reference, trace one failing case by hand before changing random lines.

• Trace first: walk one failing input step by step
• Read the manual: skim the official doc for the mechanism named in this task
• Compare baselines: save measurements from the prior step so speedups are honest

Why for this exercise

You will read a byte offset and block size from stdin and print the block index plus in-block offset. This exercise asks you to implement the mapping every page-oriented storage engine uses.

Your Task

Disks and file systems address data in fixed-size blocks. Turn a byte offset into the block that holds it and the position inside that block.

Input

Two integers: a byte offset (0 or more) and a block size (more than 0).

Output

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for 1808 512: block = offset / block size (integer division), offset = offset % block size.