Number Base Converter

Convert between binary, octal, decimal, and hexadecimal — free, instant

Base 2 — Binary
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Base 8 — Octal
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Base 10 — Decimal
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Base 16 — Hexadecimal
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Number Systems Explained

A number base (or radix) defines how many unique digits a system uses. The decimal system we use daily has base 10 (digits 0–9). Computers use binary (base 2) internally, while programming commonly uses hexadecimal (base 16) for compact representation of binary data.

Binary (Base 2)

Uses only 0 and 1. The native language of computers. Every file, image, and program is stored as a sequence of bits. 1 byte = 8 bits = 00000000 to 11111111.

Octal (Base 8)

Uses digits 0–7. Historically used in Unix file permissions (chmod 755). Each octal digit represents exactly 3 binary bits.

Decimal (Base 10)

The standard human number system using digits 0–9. The result of having 10 fingers. Natural for arithmetic but not native to computers.

Hexadecimal (Base 16)

Uses 0–9 and A–F. One hex digit = 4 binary bits (a nibble). Two hex digits = 1 byte. Widely used for colors (#FF5733), memory addresses, and binary data.

Frequently Asked Questions

Why do programmers use hexadecimal?
Hex provides a compact way to represent binary data. Each hex digit maps exactly to 4 bits, so 2 hex digits represent 1 byte. It is much more readable than long binary strings and is used for color codes, memory addresses, and binary file inspection.
How do I convert binary to decimal manually?
Each binary digit (from right) represents a power of 2. Multiply each bit by its power and sum them. For 1010: (1×8) + (0×4) + (1×2) + (0×1) = 10.
What are Unix file permission numbers?
chmod 755 means: owner=7 (rwx), group=5 (r-x), others=5 (r-x). These octal numbers come from binary: 7=111 (all permissions), 5=101 (read+execute), 4=100 (read only).
What is 0xFF in decimal?
0xFF = 255 in decimal. It is the maximum value of a single byte (8 bits = 11111111 in binary).

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