Converting a decimal number to hexadecimal is a process that translates numbers from the base-10 system (decimal) to the base-16 system (hexadecimal). The hexadecimal system is widely used in computing and programming because it offers a more human-friendly representation of binary-coded values. Each hexadecimal digit can represent four binary digits (bits), making it a compact way to express binary numbers.
Understand Hexadecimal Basics
Hexadecimal Number System. uses sixteen distinct symbols: 0-9 to represent values zero to nine, and A-F to represent values ten to fifteen. Each position in a hexadecimal number represents a power of 16.
Division-Remainder Method for Hexadecimal Conversion
This method involves dividing the decimal number by 16 repeatedly until the quotient is 0, and recording the remainders at each step. These remainders, when read in reverse order (from last to first), give you the hexadecimal equivalent.
The process of conversion
- Divide the Decimal Number by 16: Start with your decimal number and divide it by 16.
- Record the Remainder: Write down the remainder. If the remainder is between 10 and 15, write down the corresponding hexadecimal character (A to F).
- Update the Quotient: Use the quotient (the result of the division) as the new number to be divided by 16.
- Repeat the Process: Continue dividing the new quotient by 16 and recording the remainders until the quotient is 0.
- Compile the Hexadecimal Number: The hexadecimal number is read from the last remainder recorded to the first, forming a sequence from bottom to top.
Example Conversion
Let’s convert the decimal number 1256 to hexadecimal:
- 1256 ÷ 16 = 78 remainder 8
- 78 ÷ 16 = 4 remainder 14 (E)
- 4 ÷ 16 = 0 remainder 4 Reading the remainders from bottom to top, we get 4E8. Therefore, the decimal number 1256 converts to the hexadecimal number 4E8.
Verification
To ensure the accuracy of your conversion, you can verify the result by converting the hexadecimal number back to decimal. Multiply each digit of the hexadecimal number by 16 raised to the power of its position (starting from 0 on the right) and summing these values. For example, to verify 4E8:
- 8 X 16^0 = 8
- E X 16^1 = 224
- 4 X 16^2 = 1024
- Total = 8 + 224 + 1024 = 1256
Conclusion
Converting decimal numbers to hexadecimal is an essential skill in fields like computer science and digital electronics, where it simplifies the representation and understanding of binary data. By following the division-remainder method and understanding the base-16 system, you can efficiently perform these conversions and apply them in various computing contexts.