Number Base Converter
Convert numbers between different bases including binary (2), octal (8), decimal (10), hexadecimal (16), and any custom base from 2 to 36. Perfect for computer science, programming, and mathematics.
Universal Number Converter
Convert between any number bases from 2 to 36.
Common Uses for Number Base Conversion
Computer Programming
Convert between binary, hexadecimal, and decimal for memory addresses, bit operations, and data representation.
Digital Electronics
Binary and hexadecimal conversions are essential for understanding digital circuits and logic gates.
Web Development
Hexadecimal is used for color codes, while binary helps understand data encoding and file formats.
Network Administration
IP addresses, subnet masks, and MAC addresses often require hexadecimal and binary conversions.
Mathematics Education
Learn about different number systems and positional notation in computer science courses.
Cryptography
Various number bases are used in encryption algorithms and hash functions.
Popular Number System Conversions
Binary to Octal
Binary to Decimal
Binary to Hexadecimal
Octal to Binary
Octal to Decimal
Octal to Hexadecimal
Decimal to Binary
Decimal to Octal
Decimal to Hexadecimal
Hexadecimal to Binary
Hexadecimal to Octal
Hexadecimal to Decimal
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Understanding Number Systems
A number system (or numeral system) is a mathematical notation for representing numbers using a consistent set of digits or symbols. Each number system has a base (or radix) that determines how many unique digits are used and the place value of each position.
General Conversion Formula
Where di represents the digit at position i, and the rightmost position is 0.
Popular Number Systems
Binary (Base-2)
Digits: 0, 1
Used in: Computer systems, digital electronics
Example: 1011โ = 1ร2ยณ + 0ร2ยฒ + 1ร2ยน + 1ร2โฐ = 11โโ
Octal (Base-8)
Digits: 0-7
Used in: Unix file permissions, some programming
Example: 157โ = 1ร8ยฒ + 5ร8ยน + 7ร8โฐ = 111โโ
Decimal (Base-10)
Digits: 0-9
Used in: Everyday mathematics, human counting
Example: 342โโ = 3ร10ยฒ + 4ร10ยน + 2ร10โฐ = 342โโ
Hexadecimal (Base-16)
Digits: 0-9, A-F (A=10, B=11, C=12, D=13, E=14, F=15)
Used in: Programming, color codes, memory addresses
Example: 2AFโโ = 2ร16ยฒ + 10ร16ยน + 15ร16โฐ = 687โโ
Conversion Methods
Method 1: Direct Conversion (Any Base โ Decimal)
Use positional notation to convert any base to decimal:
Example: Convert 1A3โโ to decimal
Method 2: Division Method (Decimal โ Any Base)
Repeatedly divide by target base and collect remainders:
Example: Convert 157โโ to binary
Read remainders upward:
10011101โ
Method 3: Two-Step Conversion (Base A โ Base B)
For conversions between non-decimal bases:
Step 1: Convert Base A โ Decimal
Step 2: Convert Decimal โ Base B
This universal method works for any base conversion, though direct methods exist for specific pairs (like binary โ octal, binary โ hexadecimal).