Number Base Converter
Convert numbers between binary, octal, decimal, and hexadecimal instantly. Supports large integers. Free, 100% in your browser.
Reference
What are number bases?
A number base (or radix) determines how many unique digits a positional numeral system uses. Humans count in base 10 (decimal) using digits 0–9. Computers operate in base 2 (binary) using only 0 and 1 — every piece of digital data is ultimately represented as binary. Hexadecimal (base 16) and octal (base 8) provide human-readable shorthand for binary data, since their bases are powers of 2 (16 = 2⁴, 8 = 2³), making conversion straightforward.
Base reference guide
Binary (base 2): Digits 0–1. Each digit is one bit. 8 bits = 1 byte (values 0–255). Foundation of all digital computing — processors, memory, and storage all operate in binary.
Octal (base 8): Digits 0–7. Each octal digit represents exactly 3 bits. Used for Unix/Linux file permissions (chmod 755 = rwxr-xr-x).
Decimal (base 10): Digits 0–9. The standard everyday counting system — what humans use naturally.
Hexadecimal (base 16): Digits 0–9 then A–F. Each hex digit represents exactly 4 bits (one nibble). Two hex digits = one byte. Used for memory addresses, CSS colors (#FF5500), MAC addresses, and byte-level data representation.
When do developers need base conversion?
CSS colors: #1A2B3C is three hex byte pairs representing Red (26), Green (43), Blue (60) in decimal. Unix permissions: chmod 755 — 7 in octal = 111 in binary (read+write+execute), 5 = 101 (read+execute). Debugging: Memory addresses, pointers, and hex dumps in debuggers (GDB, LLDB, Chrome DevTools) are displayed in hexadecimal. Networking: MAC addresses (48-bit, shown as 6 hex pairs), IPv6 addresses (128-bit hex), and subnet masks all use hex or binary. Bitwise operations: Understanding flags, bitmasks, and bit manipulation requires thinking in binary.
Privacy
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