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
Frequently Asked Questions
What is an integer base converter?
An integer base converter is a tool that converts numbers between different numeral systems (bases). For example, it can convert a decimal number (base 10) to binary (base 2), hexadecimal (base 16), octal (base 8), or any other base from 2 to 64. The utilAZ integer base converter supports all these conversions instantly and for free.
What is hexadecimal and why is it used?
Hexadecimal (hex) is a base-16 number system that uses digits 0-9 and letters A-F. It is widely used in programming because one hex digit represents exactly 4 binary bits, making it a compact and human-readable way to express binary data. Common uses include color codes (#FF5733), memory addresses, MAC addresses, and byte-level data representation.
How do I convert decimal to binary?
To convert decimal to binary manually, repeatedly divide the decimal number by 2 and record each remainder. Then read the remainders from bottom to top to get the binary result. For example, 13 in decimal: 13/2=6 R1, 6/2=3 R0, 3/2=1 R1, 1/2=0 R1, so 13 = 1101 in binary. Or simply use the utilAZ converter for instant results.
What is base 36 and where is it used?
Base 36 is a numeral system that uses digits 0-9 and letters A-Z (36 characters total). It is commonly used for generating short, compact identifiers and URL shorteners because it can represent large numbers in fewer characters than decimal. For example, the number 1,000,000 in base 36 is just "LFLS".
Can I convert large numbers (like 64-bit integers) between bases?
Yes, the utilAZ integer base converter supports large numbers including 64-bit integers. You can convert values as large as 2^64 (18,446,744,073,709,551,616) between any supported bases. The tool handles big integer arithmetic accurately without overflow or precision loss.
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
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