Number Base Converter

Convert between binary, octal, decimal, and hexadecimal with bit visualization, two's complement, IEEE 754, and bitwise operations.

Binary (base 2)

Octal (base 8)

Decimal (base 10)

Hexadecimal (base 16)0x prefix

Custom base

Bitwise Operations

Value A (decimal)

Value B (decimal)

Shift amount

What is Number Base Conversion?

Number base conversion translates numbers between different numeral systems: binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). These systems are fundamental to computing — binary represents data at the hardware level, hex is used for colors and memory addresses, and octal is used in Unix file permissions.

Common Use Cases

•Converting between hex, binary, and decimal for debugging
•Understanding binary representations of IP addresses
•Working with hex color codes and memory addresses
•Converting octal file permissions (chmod 755)
•Visualizing bit patterns for bitwise operations

Frequently Asked Questions

Why do computers use binary?

Computers use binary because digital circuits have two states: on (1) and off (0). This maps naturally to electrical signals, transistor states, and magnetic storage. All other number systems are human conveniences built on top of binary.

Why is hexadecimal used in programming?

Hex is a compact way to represent binary — each hex digit maps to exactly 4 binary bits. This makes it easy to read memory addresses, color values, and byte sequences. 0xFF is much easier to read than 11111111.