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Hexadecimal, Decimal, and Binary Conversion

The Hexadecimal Converter facilitates easy translation between hexadecimal (base-16) and decimal (base-10) number systems. Understanding these conversions is crucial in many areas of computing, such as web design (colors), programming, and data representation. This calculator focuses on Hexadecimal to Decimal and Decimal to Hexadecimal conversions, with explanations that touch upon binary as well.

⚙️ How to Use the Converter

1. Select Conversion Mode: Choose whether you want to convert "Hex to Decimal" or "Decimal to Hex".
2. Enter Value:
   • If "Hex to Decimal": Input a hexadecimal string (e.g., 1A3F). Valid characters are 0-9 and A-F (case-insensitive).
   • If "Decimal to Hex": Input a non-negative decimal integer (e.g., 6719).
3. Click "Convert": The calculator will perform the conversion.
4. View Result: The converted value will be displayed, along with a step-by-step visual calculation.

🔄 Hexadecimal to Decimal Conversion

Hexadecimal uses 16 symbols: 0-9 and A-F (where A=10, B=11, C=12, D=13, E=14, F=15). Each position in a hexadecimal number represents a power of 16.

Example: Convert hexadecimal 2B5₁₆ to decimal.

• 2 × 16² = 2 × 256 = 512
• B (which is 11) × 16¹ = 11 × 16 = 176
• 5 × 16⁰ = 5 × 1 = 5

Sum = 512 + 176 + 5 = 693. So, 2B5₁₆ = 693₁₀.

Our calculator's "Visual Calculation" breaks this down for your input.

🔄 Decimal to Hexadecimal Conversion

This involves repeatedly dividing the decimal number by 16 and recording the remainders. The hexadecimal digits are the remainders read in reverse order.

Example: Convert decimal 693₁₀ to hexadecimal.

• 693 ÷ 16 = 43 remainder 5
• 43 ÷ 16 = 2 remainder 11 (which is B in hex)
• 2 ÷ 16 = 0 remainder 2

Reading remainders from bottom up: 2B5. So, 693₁₀ = 2B5₁₆.

The "Visual Calculation" section illustrates this process.

💡 Common Use Cases

• Web Development: Defining colors (e.g., #FF0000 for red).
• Programming: Representing memory addresses, data values, or bitmasks.
• Computer Graphics: Specifying color values.
• Data Representation: A more compact way to represent binary data (since one hex digit represents 4 binary bits).
• Assembly Language: Often used in low-level programming.

✨ Further Explanation: Hexadecimal and Binary

Hexadecimal is particularly useful because it provides a human-friendly way to represent binary numbers. Each hexadecimal digit corresponds to a unique 4-bit binary sequence:

This relationship makes it easy to convert between binary and hexadecimal. For example, the binary number 11010110 can be grouped into 4-bit chunks: 1101 and 0110.1101 is D in hex, and 0110 is 6 in hex. So, 11010110₂ = D6₁₆.

While this specific calculator focuses on Hex ⇔ Decimal, understanding the binary link is key to appreciating hexadecimal's role in computing.