💻 Base Converter
Number System Converter
Binary · Decimal · Octal · Hex
Convert between binary (base-2), decimal (base-10), octal (base-8), and hexadecimal (base-16). Perfect for programming, electronics, and math.
binary to decimal
hex converter
octal converter
base calculator
Converter
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Number System Conversion
Select source base, enter value → see results in all bases
Value to convert
📖 Conversion explanation
Enter a number and select its base → see step-by-step logic
Reference Table
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Decimal to Binary / Octal / Hex
Common values for quick reference
| Decimal | Binary | Octal | Hexadecimal |
|---|
How to Convert
Number System Conversion Methods
🔹 Binary → Decimal: multiply each digit by 2ⁿ
🔹 Decimal → Binary: repeated division by 2, read remainders
🔹 Octal ↔ Hex: convert via decimal or binary intermediate
🔹 Decimal → Binary: repeated division by 2, read remainders
🔹 Octal ↔ Hex: convert via decimal or binary intermediate
Binary Tip
Binary digits (bits): 1010₂ = 1×8 + 0×4 + 1×2 + 0×1 = 10
Octal Tip
Each octal digit = 3 bits. 17₈ = 001 111₂ = 1111₂ = 15
Hex Tip
A=10, B=11, C=12, D=13, E=14, F=15. 1F₁₆ = 31
FAQs
How do I convert binary to decimal?+
Multiply each binary digit by 2 raised to its position power (from right, starting at 0). Example: 1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8+0+2+1=11.
What is hexadecimal used for?+
Hex is widely used in computing to represent memory addresses, color codes (e.g., #FF5733), and machine code because each hex digit represents 4 bits.
Can this converter handle fractions or negative numbers?+
This version handles positive integers. For fractions, use separate scientific tools. Negative numbers can be represented using two's complement, not implemented here.
How to convert octal to hexadecimal?+
Convert octal → decimal → hex, or octal → binary (group 3 bits) → group into 4 bits → hex. Our calculator does it automatically.