Type in any box to convert between Decimal, Binary, Hex, and Octal in real time. Fast, simple, and handles huge numbers without precision loss.
Common Numbers:
0 - 9
6 bits
0-9, a-f
0 - 7
💡 How Number Bases Work in Plain Words:
A base determines when a number rolls over to the next digit. Decimal rolls over at 10 (0-9). Binary rolls over at 2 (using only 0 and 1). Hexadecimal rolls over at 16, using a through f for 10 through 15 (e.g. 0xFF = 255).
Positional base systems represent numbers using different counts of digits. While decimal is universal for humans, computers rely on binary and hexadecimal.
The Four Core Bases
十进制 (Decimal · Base 10)：Uses digits 0–9. The everyday counting system used by humans worldwide.
二进制 (Binary · Base 2)：Uses only 0 and 1. Reflects the hardware on/off states of computer transistors.
十六进制 (Hexadecimal · Base 16)：Uses 0–9 and a–f. Exactly 2 hex characters represent 1 byte (8 bits), widely used in web color codes like #FFFFFF.
八进制 (Octal · Base 8)：Uses 0–7. Commonly seen in Unix/Linux file permissions like 755 or 644.
Why Do We Have Base58 and Base62?
Base62 combines digits and upper/lowercase letters to compress long database IDs into compact short-URL slugs. Bitcoin Base58 deliberately removes visually confusable characters (0, O, I, l) to prevent costly transcription errors.