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How to Use the Number Base Converter
Step-by-Step Instructions Enter Your Number: Type the number you want to convert in the input field. Select Input Base: Choose the base (radix) of your input number from the dropdown: Binary (Base 2): Uses digits 0-1 Octal (Base 8): Uses digits 0-7 Decimal (Base 10): Uses digits 0-9 Hexadecimal (Base 16): Uses digits 0-9 and A-F Other bases from 2 to 36 available Convert: Click "Convert" or type to see instant conversions to all common bases. View Results: See your number converted to: Common bases (2, 8, 10, 16) Extended bases (3-36) Custom base of your choice Copy Results: Click the copy button next to any result to copy it to clipboard. Analyze: View properties and breakdown of your number below. Understanding Number Bases
Binary (Base 2) The fundamental language of computers, using only 0 and 1. Digits: 0, 1 Place Values: ...8, 4, 2, 1 (powers of 2) Example: 1101₂ = 1×8 + 1×4 + 0×2 + 1×1 = 13₁₀ Usage: Computer programming, digital electronics, data representation Octal (Base 8) Compact representation using digits 0-7, often used in Unix permissions. Digits: 0, 1, 2, 3, 4, 5, 6, 7 Place Values: ...512, 64, 8, 1 (powers of 8) Example: 175₈ = 1×64 + 7×8 + 5×1 = 125₁₀ Usage: File permissions, legacy computing, shorthand for binary Decimal (Base 10) The standard number system used in everyday life. Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Place Values: ...1000, 100, 10, 1 (powers of 10) Example: 245₁₀ = 2×100 + 4×10 + 5×1 Usage: Mathematics, commerce, daily calculations Hexadecimal (Base 16) Efficient way to represent binary data, widely used in programming. Digits: 0-9, A-F (where A=10, B=11, ..., F=15) Place Values: ...4096, 256, 16, 1 (powers of 16) Example: 2AF₁₆ = 2×256 + 10×16 + 15×1 = 687₁₀ Usage: Color codes, memory addresses, cryptography Conversion Methods
Converting TO Decimal Multiply each digit by its place value and sum:
Example: 1101₂ to Decimal Converting FROM Decimal Repeatedly divide by the target base, collect remainders:
Example: 13₁₀ to Binary Binary ↔ Hex Shortcut Group binary digits in sets of 4:
Example: 11010111₂ to Hex Binary ↔ Octal Shortcut Group binary digits in sets of 3:
Example: 110101₂ to Octal Common Applications
Web Design Color Codes: #FF0000 (red in hex) RGB Values: rgb(255, 0, 0) Transparency: #FF0000AA (with alpha) Computer Science Memory Addresses: 0x7FFF0000 Bitwise Operations: AND, OR, XOR Data Representation: ASCII, Unicode Cryptography Hash Values: SHA-256 in hex Keys: Base64 encoding Checksums: MD5, CRC32 Networking IP Addresses: Dotted decimal MAC Addresses: Hex pairs Subnet Masks: Binary patterns Quick Reference Tables
Common Conversions
Decimal
Binary
Octal
Hex
Powers Reference
Power
2ⁿ
8ⁿ
16ⁿ
Frequently Asked Questions
Why do programmers use hexadecimal? Hexadecimal is more compact than binary (4 bits = 1 hex digit) and easier to read than long binary strings. It's also easy to convert between hex and binary mentally, making it ideal for representing binary data like memory addresses and color values. What bases can use letters? Any base greater than 10 uses letters. Base 11 uses 0-9 and A, base 12 uses 0-9 and A-B, and so on up to base 36 which uses 0-9 and A-Z. Letters are case-insensitive. What's the largest base supported? Base 36 is the practical maximum, using all digits 0-9 and letters A-Z. This gives 36 unique symbols. Higher bases would require additional symbols beyond the standard alphabet. How do I convert between any two non-decimal bases? The easiest method is to convert to decimal as an intermediate step. Convert from the source base to decimal, then from decimal to the target base. Direct conversion is possible but more complex. What are common mistakes in base conversion? Common errors include: forgetting that digits must be less than the base (e.g., 8 is invalid in octal), confusing letter values in hex (A=10, not 1), and misaligning place values when converting. Tips & Tricks
Quick Mental Conversions Binary to Hex: Group by 4 bits from right Binary to Octal: Group by 3 bits from right Hex F = Binary 1111 = Decimal 15 Powers of 2: 2, 4, 8, 16, 32, 64, 128, 256... Double-check: Converting back should give original Input Tips Letters in bases >10 are case-insensitive No spaces or commas in numbers Leading zeros are ignored Use standard notation (no subscripts needed) Decimal point not supported (integers only) Verification Methods Convert result back to verify accuracy Check digit validity for the base Use multiple methods to confirm Test with known values first Watch for overflow in large numbers (责任编辑：) |