Binary, Decimal, Hex & Octal — Number Bases Explained
Humans count in tens because we have ten fingers; computers count in twos because a transistor knows two states. Everything else — hexadecimal, octal, the colour codes in your CSS, the MAC address on your router — is just humans and computers meeting in the middle. This guide explains how bases actually work, why hex exists at all, and how to convert any number between bases with LND AI’s free converter.
How a base works
A number system’s base is how many symbols it uses before it carries. Base 10 has symbols 0–9: after 9 you carry and write 10. Base 2 (binary) has symbols 0–1: after 1 you carry. Base 16 (hexadecimal) needs sixteen symbols, so after 9 it borrows letters: A=10, B=11, C=12, D=13, E=14, F=15. The value of any position is its digit × base to the power of its position — 1011 in binary is 1×8 + 0×4 + 1×2 + 1×1 = eleven.
The deep point: numbers themselves are base-less. "Eleven" is a quantity; 11, 1011 and B are three notations for it. Converting between bases is translation, not calculation — the quantity never changes, only its clothing.
Why hexadecimal exists at all
Binary is what hardware speaks, but binary is unreadable to humans — 11111110 means nothing at a glance. Hex is the compromise: because 16 is exactly 4 bits, every hex digit corresponds to exactly one nibble. 11111110 splits into 1111 1110 → F E → FE. Two hex characters per byte, always — which is why MAC addresses, colour codes, memory addresses and hex dumps are written in hex rather than binary or decimal. Hex is binary compressed for human eyes.
| Base | Symbols | Where you meet it |
|---|---|---|
| 2 (binary) | 0, 1 | Hardware logic, bitwise operations, flags |
| 8 (octal) | 0–7 | Unix file permissions (chmod), legacy systems |
| 10 (decimal) | 0–9 | Everything human |
| 16 (hex) | 0–9, A–F | Colours, MACs, addresses, hex dumps, debuggers |
Converting by hand (once, for the feel of it)
Decimal to binary: repeatedly divide by 2 and collect remainders. Twenty-two → 22÷2 = 11 r0, 11÷2 = 5 r1, 5÷2 = 2 r1, 2÷2 = 1 r0, 1÷2 = 0 r1 — reading remainders bottom-up gives 10110. Binary to decimal: sum digit × 2-position. Binary to hex: group in fours from the right and translate each group. Do each once to feel the mechanics, then let the converter do it forever after — the point of understanding is trust, not labour.
Using LND AI Binary Converter
- Open the toolGo to namansoni.in/binary-converter — completely free, no sign-up, conversions run in your browser.
- Enter a numberType a value in any base — binary, decimal, hexadecimal or octal.
- See all bases at onceThe converter shows the number in every base simultaneously, so relationships are visible, not just answers.
- Copy what you needTake the representation your context wants — bits for flags, hex for colours, decimal for humans.
Where you will actually use this
- Colour codes:
#8B5CF6is three bytes in hex — R=139, G=92, B=246. The Color Converter tool completes this picture. - Debugging: reading flags, masks and register values straight out of debuggers and logs.
- Bitwise logic: checking which bits are set in a permission or configuration value.
- Networking: IP subnetting and MAC addresses are hex-heavy territory.
- Learning: genuinely understanding bases once makes every later CS topic — two’s complement, bitwise ops, alignment — click into place.
Frequently asked questions
How do you convert binary to decimal?
Sum each digit multiplied by 2 raised to its position from the right, starting at zero: 1011 = 1×8 + 0×4 + 1×2 + 1×1 = 11. Or skip the arithmetic entirely — namansoni.in/binary-converter shows binary, decimal, hex and octal simultaneously as you type.
Why do programmers use hexadecimal instead of binary?
Because 16 is exactly 4 bits, every hex digit maps to precisely one binary nibble — two hex characters always equal one byte. Binary is unreadable at length, and hex is its faithful compression: 11111110 becomes FE with zero ambiguity. That is why colours, MAC addresses, memory addresses and hex dumps are written in hex.
What do the letters in hexadecimal mean?
Hex needs sixteen symbols; after 0–9 it borrows A–F for the values 10 through 15: A=10, B=11, C=12, D=13, E=14, F=15. So F is the largest single hex digit, and FF — two digits — is 255, the maximum value of one byte.
What is octal still used for?
Most visibly, Unix file permissions: three bits per permission class map perfectly onto one octal digit, so rwx = 111 = 7 and chmod 754 encodes rwxr-xr-- compactly. Octal otherwise survives mainly in legacy computing contexts.
What is the largest number in one byte?
255 — eight bits all set: 11111111 in binary, FF in hex. It is why colour channels max at 255, why old game scores rolled over at 255, and why IP octets stop at 255. Two bytes reach 65535.