Numbers in computing
Computing is built on the binary (base-2) number system and its powers — 8, 16, 32, 64 and beyond — which is why specific numbers like 0, 1, 8, 64 and 404 keep appearing throughout technology.
Some numbers here (0, 1, 2) are the binary number system itself; others (8, 16, 64) are specific bit-widths built from powers of two; 404 is a specific protocol convention, not a mathematical necessity. This hub groups them by their shared role in computing, not by any mathematical property they have in common.
Why computers use 0 and 1
Binary (base-2) represents every value using only two digits, matching the two reliable states of a digital switch — off/on, or low/high voltage. Every other numeral system used in computing (hexadecimal, for instance) is really just a more compact way of writing the same underlying binary values, not a different way of storing them.
Bytes and bit-widths
A byte is defined as 8 bits — enough to represent 256 distinct values (2⁸), which historically made it a convenient unit for a single character of text. Processor and software architectures are described by how many bits they handle at once: 16-bit and 32-bit were common through the 1980s-2000s, and 64-bit is the dominant standard today.
These bit-widths are all powers of two because binary hardware naturally doubles its range with each additional bit — there's no equivalent reason to standardise on, say, 20-bit or 50-bit.
Conventions vs necessity: 404 and HTTP status codes
Unlike binary and bit-widths, HTTP status codes like 404 aren't derived from any mathematical property — they're a documented protocol convention agreed on by the engineers who designed the web's HTTP standard. The specific number 404 was simply assigned to the "resource not found" response; a different number could have been chosen without changing anything about how computers work.
Numbers featured in this hub
Common questions
Why do computers use 0 and 1?
Digital electronic circuits are built from switches that are most reliably read as one of two states (on/off, high/low voltage) — representing those two states as the digits 0 and 1 (binary, base-2) is simpler and more error-resistant than trying to distinguish many voltage levels reliably.
Why does programming often count from 0?
In many languages, an array index is really an offset — how far a value sits from the start of a block of memory. The first item sits 0 positions from the start, which is why counting from 0 (not 1) matches how the underlying memory address is actually calculated.
Why are 8, 16, 32 and 64 important in computing?
Each is a power of two (2³, 2⁴, 2⁵, 2⁶), the natural unit sizes for binary hardware. 8 bits make a byte; 16, 32 and 64-bit describe how much data a processor or piece of software can handle at once, with 64-bit the current dominant standard.
Why is 404 'Not Found'?
404 is simply the specific number the HTTP protocol's original designers assigned to the 'resource not found' response — a documented convention, not a mathematical necessity. Different number ranges (1xx, 2xx, 3xx, 4xx, 5xx) group different categories of response.
What is the difference between 1000 and 1024 in storage?
1000 is the decimal (SI) meaning of 'kilo'; 1024 (2¹⁰) is the binary meaning some storage/memory contexts historically used for the same prefix — a real, frequently confused distinction, though this hub does not yet cover a dedicated 1024 profile.