Converting hexadecimal (hex) to decimal involves translating numbers from the base-16 system (hexadecimal) to the base-10 system (decimal). Hexadecimal numbers include the digits 0 through 9 and the letters A through F, which represent the decimal values 10 through 15, respectively.
Step-by-Step Conversion Overview
- List Hexadecimal Digits: Start by writing down the hex number, identifying each digit and its place value. Remember, hex digits from right to left represent increasing powers of 16.
- Convert Hex Digits to Decimal: Convert each hex digit to its decimal equivalent. Numbers 0-9 retain their value, while letters A-F are converted to 10-15.
- Apply Place Values: Multiply each decimal digit by 16 raised to the power of its position, counting from 0 at the rightmost digit.
- Sum the Results: Add all the values obtained in the previous step to get the final decimal number.
Detailed Conversion Process
To illustrate, let’s convert the hexadecimal number 1A3 to decimal:
- The hex digit 1 converts to 1 in decimal.
- The hex digit A converts to 10 in decimal.
- The hex digit 3 converts to 3 in decimal.
- Applying place values: 1 x 16^2 + 10 x 16^1 + 3 x 16^0 = 1 x 256 + 10 x 16 + 3 x 1 = 256 + 160 + 3 = 419.
Therefore, the hexadecimal number 1A3 converts to the decimal number 419.
Practical Insights
This method of conversion from hex to decimal reveals the structured relationship between different numeral systems and underscores the importance of base conversions in computing and digital electronics. Understanding how to perform these conversions allows for a deeper comprehension of how data is represented and manipulated within computer systems.