Why do computers use binary instead of decimal?

Electronic circuits have two stable states: on and off, which map naturally to 1 and 0. Binary arithmetic can be implemented with simple logic gates, making it far more practical than base-10 for hardware.

Why is hexadecimal used in programming?

Each hex digit represents exactly 4 bits, so two hex digits represent one byte. This makes hex a compact and readable way to express binary data, memory addresses, and color values.

How do I convert hex to binary?

Replace each hex digit with its 4-bit binary equivalent: 0=0000, 1=0001, ..., A=1010, ..., F=1111. For example, 0xFF = 1111 1111 and 0xA3 = 1010 0011.

Binary, Decimal, and Hex Conversion

Understanding number base conversions is fundamental to low-level programming, networking, and computer science. Binary (base-2), decimal (base-10), hexadecimal (base-16), and octal (base-8) all represent the same values in different notation systems. This collection shows conversions for common programming values: byte boundaries, permission bits, and color components. The binary-to-decimal converter shows each step of the positional weighting calculation so you can internalize the pattern rather than just looking up the result.

Example

# Decimal to Binary
255 = 11111111 (0xFF, 8 bits all set)
128 = 10000000 (0x80, high bit)
127 = 01111111 (0x7F, max signed byte)
64  = 01000000 (0x40)
32  = 00100000 (0x20)

# Unix permissions
777 (octal) = 111 111 111 (binary) = rwxrwxrwx
644 (octal) = 110 100 100 (binary) = rw-r--r--
755 (octal) = 111 101 101 (binary) = rwxr-xr-x

[ open in Binary to Decimal → ]

FAQ

Why do computers use binary instead of decimal?: Electronic circuits have two stable states: on and off, which map naturally to 1 and 0. Binary arithmetic can be implemented with simple logic gates, making it far more practical than base-10 for hardware.
Why is hexadecimal used in programming?: Each hex digit represents exactly 4 bits, so two hex digits represent one byte. This makes hex a compact and readable way to express binary data, memory addresses, and color values.
How do I convert hex to binary?: Replace each hex digit with its 4-bit binary equivalent: 0=0000, 1=0001, ..., A=1010, ..., F=1111. For example, 0xFF = 1111 1111 and 0xA3 = 1010 0011.

Related Examples

Hex Color Value Examples

Hex color codes are the most common way to specify colors in CSS and design tool...

Percentage Calculation Examples

Percentage calculations appear constantly in e-commerce (discounts), finance (in...

Hex Dump and Text-to-Hex Encoding

A hex dump shows the hexadecimal byte values of text or binary data alongside it...