Number Base Converter Tool

Number Base Converter

Convert between binary, decimal, and hexadecimal number systems

Binary (Base 2)

Uses only 0 and 1. Example: 1010 converts to decimal 10 and hex A. Each digit represents a power of 2 (from right: 1, 2, 4, 8, 16...).

Decimal (Base 10)

Uses digits 0-9. Example: 42 converts to binary 101010 and hex 2A. Each digit represents a power of 10 (from right: 1, 10, 100, 1000...).

Hexadecimal (Base 16)

Uses digits 0-9 and letters A-F. Example: 2A converts to binary 101010 and decimal 42. Each digit represents a power of 16 (from right: 1, 16, 256, 4096...).

About Number Systems

Binary System (Base 2)

Example: 1010 (binary) = 10 (decimal) = A (hex)

Conversion: Sum powers of 2 where digit is 1. 1010 = (1×8) + (0×4) + (1×2) + (0×1) = 10.

The fundamental language of computers. Each binary digit (bit) represents an on/off state. Eight bits make a byte (can represent 0-255).

Decimal System (Base 10)

Example: 42 (decimal) = 101010 (binary) = 2A (hex)

Conversion to binary: Divide by 2 and record remainders: 42 → 101010.

The standard human numbering system. Used in everyday counting. Each position represents a power of 10, making arithmetic intuitive.

Hexadecimal System (Base 16)

Example: 2A (hex) = 42 (decimal) = 101010 (binary)

Conversion: 2A = (2×16) + (10×1) = 42. Each hex digit represents exactly 4 binary digits (nibble).

Widely used in computing as a compact representation of binary. One hex digit = 4 bits, two hex digits = 1 byte (8 bits).

Conversion Examples

Binary	Decimal	Hexadecimal
0000	0	0
0001	1	1
1010	10	A
1111	15	F
101010	42	2A
11111111	255	FF