Binary, hex and other bases: one number, many spellings

Number science. 6-minute read. Updated 2026-10-10.

36118 is a quantity. "36118" is one way to write it, using base 10. Change the base and the same quantity gets a different spelling.

How a base works

In base 10 each position is worth ten times the one to its right: 36118 means 3×10,000 + 6×1,000 + 1×100 + 1×10 + 8×1. In base 2 each position is worth twice the one to its right; in base 16, sixteen times.

36118 in other bases

Converting by hand

Divide by the base, write down the remainder, and repeat with the quotient until it reaches zero. Reading the remainders from last to first gives the answer. For hexadecimal: 36118 ÷ 16 = 2257 remainder 6; 2257 ÷ 16 = 141 remainder 1; 141 ÷ 16 = 8 remainder 13 (D); 8 ÷ 16 = 0 remainder 8. Reading upward: 8D16.

Why computers love binary and hex

Electronic circuits are reliable at telling two states apart, so binary is natural for hardware. Hexadecimal is a compact shorthand: each hex digit stands for exactly four binary digits, so 8D16 maps to 1000 1101 0001 0110. That is why colours (#13233F), memory addresses and file signatures are written in hex.

Base 36 and short links

Base 36 uses 0–9 and A–Z. It packs numbers into short, case-insensitive strings, which is why it turns up in URL shorteners and order codes.

The number decoder converts any number up to 15 digits into all four bases instantly.

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