Base Number Converter
Convert numbers between binary, octal, decimal, and hexadecimal instantly. Free online base converter for programmers and students.
Binary (Base 2)
0b11111111Octal (Base 8)
0o377Decimal (Base 10)
255Hexadecimal (Base 16)
0xFFTry these:
Binary, Octal, Decimal, Hex Conversion Table
Complete reference table for converting between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16).
How to Convert Between Number Bases
Binary to Decimal
1010₂ → (1×2³) + (0×2²) + (1×2¹) + (0×2⁰) = 8 + 0 + 2 + 0 = 10₁₀
Multiply each digit by 2 raised to its position power (right to left, starting at 0). Sum all results.
Decimal to Binary
13₁₀ → 13÷2=6 R1, 6÷2=3 R0, 3÷2=1 R1, 1÷2=0 R1 → read up: 1101₂
Divide by 2 repeatedly, record remainders. Read remainders from bottom to top.
Hex to Binary (shortcut)
0xFA → F=1111, A=1010 → 11111010₂
Replace each hex digit with its 4-bit binary equivalent. This is why hex is so popular — direct 1:4 mapping with binary.
Binary to Hex (shortcut)
11111111₂ → 1111 1111 → F F → FF₁₆ = 255₁₀
Group binary digits into chunks of 4 (from right). Convert each group to hex.
Hexadecimal Digit Reference
ASCII Character Number Values
Base Conversion in Code
// Decimal to other bases
(255).toString(2); // "11111111" (binary)
(255).toString(8); // "377" (octal)
(255).toString(16); // "ff" (hex)
// Other bases to decimal
parseInt("11111111", 2); // 255
parseInt("377", 8); // 255
parseInt("FF", 16); // 255
// Literals
const bin = 0b11111111; // 255
const oct = 0o377; // 255
const hex = 0xFF; // 255# Decimal to other bases
bin(255) # '0b11111111'
oct(255) # '0o377'
hex(255) # '0xff'
# Other bases to decimal
int('11111111', 2) # 255
int('377', 8) # 255
int('FF', 16) # 255
# Literals
b = 0b11111111 # 255
o = 0o377 # 255
h = 0xFF # 255Where Each Number Base is Used
Binary (Base 2)
- • All digital computing and electronics
- • Network subnet masks (255.255.255.0 = 11111111.11111111.11111111.00000000)
- • Bit flags and bitwise operations in programming
- • Machine code and CPU instructions
Octal (Base 8)
- • Unix/Linux file permissions (chmod 755)
- • Some programming languages (C, Java octal literals)
- • Legacy computing systems (PDP-11, early Unix)
Decimal (Base 10)
- • Everyday counting and arithmetic
- • User-facing values in software
- • Financial calculations
- • Most human-readable data
Hexadecimal (Base 16)
- • CSS color codes (#FF0000, #00FF00)
- • Memory addresses and pointers
- • MAC addresses (AA:BB:CC:DD:EE:FF)
- • Unicode code points (U+0041 = 'A')
- • RGB color values in design tools
- • Debugging and hex editors
Frequently Asked Questions
What is a base converter?
A base converter (number base converter) converts numbers between different numeral systems — binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). These are the most commonly used bases in computer science and programming.
What is binary (base 2)?
Binary uses only two digits: 0 and 1. It is the fundamental number system for all computers and digital electronics. Every piece of data in a computer — text, images, video — is ultimately stored as binary.
What is hexadecimal (base 16)?
Hexadecimal uses digits 0-9 and letters A-F (where A=10, B=11, ... F=15). It is used in programming for memory addresses, color codes (#FF0000 = red), and representing binary data compactly. One hex digit = exactly 4 binary digits.
What is octal (base 8)?
Octal uses digits 0-7. It is used in Unix/Linux file permissions (chmod 755), some programming languages, and legacy computing systems. One octal digit = exactly 3 binary digits.
How do I convert binary to decimal?
Multiply each binary digit by its positional power of 2 and sum. For 1010: (1×8) + (0×4) + (1×2) + (0×1) = 8 + 0 + 2 + 0 = 10 in decimal.
How do I convert decimal to binary?
Repeatedly divide by 2 and record remainders. 13 ÷ 2 = 6 R1, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1. Read remainders bottom-up: 1101.
How do I convert decimal to hexadecimal?
Repeatedly divide by 16 and record remainders. 255 ÷ 16 = 15 R15. 15 ÷ 16 = 0 R15. Remainders: 15,15 → FF in hex. Or group binary into 4-bit chunks: 11111111 → 1111 1111 → F F → FF.
How do I convert hex to binary?
Replace each hex digit with its 4-bit binary equivalent. F = 1111, A = 1010, 0 = 0000. So 0xFA = 1111 1010 in binary. This is why hex is popular — easy conversion to/from binary.
What does 0xFF mean in programming?
0xFF is hexadecimal for 255 in decimal (11111111 in binary). The 0x prefix indicates hexadecimal notation in most programming languages (C, JavaScript, Python, Java). It represents the maximum value of a single byte (8 bits).
What is 0b prefix in programming?
0b indicates binary notation in many languages (JavaScript, Python, C++). For example, 0b1010 = 10 in decimal. Similarly, 0o prefix means octal (0o17 = 15 decimal).
Why do computers use binary?
Computers use binary because digital circuits have two states: on (1) and off (0), represented by voltage levels. This makes binary the most reliable and efficient system for electronic computation, storage, and data transmission.
How is hexadecimal used in CSS colors?
CSS hex colors use 6 hex digits: #RRGGBB. Each pair represents a color channel (0-255). #FF0000 = red (R=255, G=0, B=0). #00FF00 = green. #0000FF = blue. #FFFFFF = white. #000000 = black.
Disclaimer: This tool handles standard integer conversions between bases 2, 8, 10, and 16. For very large numbers, floating-point, or signed representations, verify with your programming environment.