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108 LearnersLast updated on October 7, 2025
Formula for Decimal to Hexadecimal Conversion
Converting a decimal number to its hexadecimal equivalent involves understanding the base-16 system. Each digit represents a power of 16, starting from the right with 16^0. In this topic, we will explore the formula and method for converting decimal numbers to hexadecimal.
Steps for Decimal to Hexadecimal Conversion
Converting decimal numbers to hexadecimal involves dividing the number by 16 and using the remainders. Let’s learn the step-by-step formula and process to perform this conversion.
Conversion Method
To convert a decimal number to hexadecimal, repeatedly divide the number by 16 and record the remainders. These remainders, read in reverse order, form the hexadecimal equivalent. The steps are as follows:
1. Divide the decimal number by 16.
2. Record the remainder.
3. Use the quotient for the next division.
4. Repeat until the quotient is zero.
5. The hexadecimal number is the remainders read in reverse order.
Example Conversion
Let’s convert the decimal number 255 to hexadecimal:
1. 255 ÷ 16 = 15 remainder 15
2. 15 ÷ 16 = 0 remainder 15
Reading the remainders from bottom to top gives us FF in hexadecimal.
Understanding Hexadecimal Digits
The hexadecimal system uses digits from 0 to 9 and letters A to F.
Each digit represents 0 to 15 in decimal, where A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15.
Importance of Decimal to Hexadecimal Conversion
Decimal to hexadecimal conversion is widely used in computing and digital electronics.
It simplifies the representation of binary values and is essential for programming, memory addressing, and more.
Tips and Tricks to Memorize Hexadecimal Values
Memorizing hexadecimal values can be tricky. Here are some tips:
- Remember the sequence: 0-9 and A-F.
- Associate letters with numbers (A=10, B=11, etc.).
- Practice with examples to reinforce learning.
- Use mnemonic devices to remember letter values.
Common Mistakes and How to Avoid Them in Decimal to Hexadecimal Conversion
Errors can occur during decimal to hexadecimal conversion. Here are common mistakes and how to avoid them.
Mistake 1
Forgetting to read remainders in reverse
A common error is not reading the remainders from bottom to top. Always remember to read them in reverse order to get the correct hexadecimal value.
Mistake 2
Incorrect division or remainder calculation
Errors in division or calculating remainders can lead to incorrect results. Double-check each division step and verify the remainder to ensure accuracy.
Mistake 3
Misinterpreting hexadecimal digits
Confusing decimal digits with hexadecimal ones, especially letters, is a frequent mistake. Remember that A-F represent 10-15 to avoid this error.
Mistake 4
Overlooking zero quotient condition
Some students forget to stop the process when the quotient reaches zero. Ensure that the conversion process halts when you reach a zero quotient.
Mistake 5
Skipping steps in conversion process
Skipping any step in the conversion process can lead to errors. Follow each step methodically to ensure a correct conversion.
Examples of Decimal to Hexadecimal Conversion Problems
Problem 1
Convert the decimal number 100 to hexadecimal.
The hexadecimal equivalent of 100 is 64.
Explanation
1. 100 ÷ 16 = 6 remainder 4 2. 6 ÷ 16 = 0 remainder 6
Reading the remainders gives us 64 in hexadecimal.
Problem 2
Convert the decimal number 250 to hexadecimal.
The hexadecimal equivalent of 250 is FA.
Explanation
1. 250 ÷ 16 = 15 remainder 10 2. 15 ÷ 16 = 0 remainder 15
Converting the remainders gives us FA in hexadecimal (A=10, F=15).
Problem 3
Convert the decimal number 45 to hexadecimal.
The hexadecimal equivalent of 45 is 2D.
Explanation
1. 45 ÷ 16 = 2 remainder 13 2. 2 ÷ 16 = 0 remainder 2
Reading the remainders gives us 2D in hexadecimal (D=13).
Problem 4
Convert the decimal number 500 to hexadecimal.
The hexadecimal equivalent of 500 is 1F4.
Explanation
1. 500 ÷ 16 = 31 remainder 4 2. 31 ÷ 16 = 1 remainder 15 3. 1 ÷ 16 = 0 remainder 1
Reading the remainders gives us 1F4 in hexadecimal (F=15).
Problem 5
Convert the decimal number 128 to hexadecimal.
The hexadecimal equivalent of 128 is 80.
Explanation
1. 128 ÷ 16 = 8 remainder 0 2. 8 ÷ 16 = 0 remainder 8
Reading the remainders gives us 80 in hexadecimal.
FAQs on Decimal to Hexadecimal Conversion
1.What is the method to convert decimal to hexadecimal?
2.What is the hexadecimal equivalent of the decimal number 255?
3.How do hexadecimal digits differ from decimal digits?
4.Why is hexadecimal used in computing?
5.How do you handle remainders when converting to hexadecimal?
Glossary for Decimal to Hexadecimal Conversion
- Decimal: The base-10 numbering system, utilizing digits 0 to 9.
- Hexadecimal: The base-16 numbering system, using digits 0-9 and letters A-F.
- Remainder: The leftover value after division, used in conversion processes.
- Quotient: The result of division, used repeatedly in conversion until it is zero.
- Base: The foundational number of a numbering system, e.g., 10 for decimal, 16 for hexadecimal.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
