Integer Base Converter
Convert numbers between different bases (2-64)
Integer Base Converter
Convert numbers between different bases (2-64)
About Number Base Conversion
Number base conversion transforms integers between different numeral systems used in mathematics, computer science, and engineering. Essential for programmers, students, and anyone working with different number representations.
- Convert between any base from 2 to 64
- Support for binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16)
- Custom bases with extended character sets
- Step-by-step conversion explanation
- Instant conversion with error validation
Common Number Systems
Binary (Base 2)
Uses digits: 0, 1
Example: 1010 = 10 in decimal
Octal (Base 8)
Uses digits: 0-7
Example: 12 = 10 in decimal
Decimal (Base 10)
Uses digits: 0-9
Example: 10 = standard counting
Hexadecimal (Base 16)
Uses: 0-9, A-F
Example: A = 10 in decimal
Base 36
Uses: 0-9, A-Z
Popular for compact representations
Base 64
Uses: A-Z, a-z, 0-9, +, /
Used in encoding systems
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Frequently Asked Questions
Why do computers use binary?
Computers use binary (base 2) because digital circuits can easily represent two states: on (1) and off (0). This makes binary the fundamental number system for all digital computing.
When is hexadecimal used?
Hexadecimal (base 16) is commonly used in programming for memory addresses, color codes (#FF5733), and representing binary data compactly. One hex digit represents exactly 4 binary digits.
What's the highest base supported?
Our converter supports bases up to 64, using characters 0-9, A-Z, a-z, +, and /. This covers all practical use cases from binary to specialized encoding systems.
How do I convert manually?
To convert from any base to decimal: multiply each digit by the base raised to its position power. To convert from decimal to any base: repeatedly divide by the target base and collect remainders.
Conversion Examples
Binary to Decimal:
1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰
= 1×8 + 0×4 + 1×2 + 1×1
= 8 + 0 + 2 + 1
= 11₁₀
Decimal to Hexadecimal:
255₁₀ ÷ 16 = 15 remainder 15 (F)
15₁₀ ÷ 16 = 0 remainder 15 (F)
Result: FF₁₆
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Programming Examples
JavaScript:
// Convert from decimal to different bases
const decimal = 255;
console.log(decimal.toString(2)); // "11111111" (binary)
console.log(decimal.toString(8)); // "377" (octal)
console.log(decimal.toString(16)); // "ff" (hexadecimal)
// Convert from any base to decimal
console.log(parseInt("11111111", 2)); // 255
console.log(parseInt("377", 8)); // 255
console.log(parseInt("ff", 16)); // 255
Python:
# Convert from decimal to different bases
decimal = 255
print(bin(decimal)) # '0b11111111'
print(oct(decimal)) # '0o377'
print(hex(decimal)) # '0xff'
# Convert from any base to decimal
print(int('11111111', 2)) # 255
print(int('377', 8)) # 255
print(int('ff', 16)) # 255
Common Use Cases
- Computer science education
- Programming and debugging
- Memory address calculations
- Color code conversions
- Network subnet calculations
- Digital electronics design
- Cryptography and encoding
- Data compression algorithms
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