Why do computers use binary (base 2)?

Digital circuits operate on two voltage levels — high and low — which map naturally to 1 and 0. Binary makes transistor design simple and noise-resistant: a signal is either clearly on or clearly off, with no ambiguity between states. Every higher-level abstraction — bytes, integers, floating-point numbers, even the text you are reading now — is ultimately stored and manipulated as sequences of binary digits. Our Encode / Decode tool lets you see exactly how text becomes binary through encodings like Base64, which uses a 64-character alphabet to represent binary data as printable ASCII.

What is hexadecimal and why is it used in programming?

Hexadecimal (base 16) uses the digits 0-9 and letters A-F to represent values 0-15 per digit. Because 16 is a power of 2 (2⁴), each hex digit maps to exactly four binary bits, making it a compact and lossless shorthand for binary data. Memory addresses, byte values, and bitwise masks are far easier to read in hex than in long binary strings — for example, 0xFF is instantly recognizable as eight set bits (11111111). Hex is also the foundation of hex color codes , where a six-digit hex value like #1A2B3C encodes red, green, and blue channels as three pairs of base-16 digits.

How can I convert between binary and hexadecimal mentally?

Group binary digits into nibbles of four bits, starting from the right, and convert each nibble to its hex equivalent (0000=0, 0001=1, ... 1001=9, 1010=A, ... 1111=F). For example, 11010110 splits into 1101 (D) and 0110 (6), giving 0xD6 . Going the other way, expand each hex digit back to four bits. This works because 16 = 2⁴, so hex and binary share a direct positional relationship — no division or modular arithmetic required.

What is octal (base 8) used for?

Octal represents three binary bits per digit (since 8 = 2³). Its most visible modern use is Unix file permissions: the familiar chmod 755 is three octal digits encoding read (4), write (2), and execute (1) bits for owner, group, and others. Octal was also the preferred human-readable base on early systems with 12-, 24-, or 36-bit word sizes that divided evenly into groups of three bits. Today decimal and hex have mostly replaced it, but you will still encounter octal literals in C, Python, and shell scripts.

What do the 0x, 0b, and 0o prefixes mean in code?

These prefixes tell the compiler or interpreter which number base you intend. 0x (or 0X ) denotes hexadecimal, 0b (or 0B ) denotes binary, and 0o (or a leading 0 in C) denotes octal. For example, 0xFF , 0b11111111 , and 0o377 all equal 255 in decimal. Languages including JavaScript, Python, Rust, Go, and Swift support all three prefixes. Use our converter above to verify these equivalences instantly.

Why do some languages use different base prefixes?

Historical fragmentation. C inherited leading-zero for octal from B (1970s), but this caused bugs when developers wrote 0777 intending decimal 777. Python 3 fixed this by requiring 0o777 for octal and raising a SyntaxError on bare leading zeros. Rust, Go, and Swift adopted the same 0b / 0o / 0x convention. JavaScript added 0b and 0o in ES2015, but watch out: parseInt("077") may return 63 (octal) in some engines — always pass a radix: parseInt("077", 10) .

Number Base Converter

Free online number base converter between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16)

Base Converter

Binary (Base 2)

0-1

Octal (Base 8)

0-7

Decimal (Base 10)

0-9

Hexadecimal (Base 16)

0-9, A-F

Enter a number in any base to convert

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Number Base Converter

Base Converter

Binary (Base 2)

Octal (Base 8)

Decimal (Base 10)

Hexadecimal (Base 16)

Frequently Asked Questions

Why do computers use binary (base 2)?

What is hexadecimal and why is it used in programming?

How can I convert between binary and hexadecimal mentally?

What is octal (base 8) used for?

What do the 0x, 0b, and 0o prefixes mean in code?

Why do some languages use different base prefixes?

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Encode

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Base Converter

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Frequently Asked Questions

Why do computers use binary (base 2)?

What is hexadecimal and why is it used in programming?

How can I convert between binary and hexadecimal mentally?

What is octal (base 8) used for?

What do the 0x, 0b, and 0o prefixes mean in code?

Why do some languages use different base prefixes?