Formula for Decimal to Hexadecimal Conversion
2026-02-28 00:53 Diff
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Last updated on October 7, 2025

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.

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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: 

  • 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.

Problem 1

Convert the decimal number 100 to hexadecimal.

Okay, lets begin

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.

Well explained 👍

Problem 2

Convert the decimal number 250 to hexadecimal.

Okay, lets begin

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).

Well explained 👍

Problem 3

Convert the decimal number 45 to hexadecimal.

Okay, lets begin

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).

Well explained 👍

Problem 4

Convert the decimal number 500 to hexadecimal.

Okay, lets begin

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).

Well explained 👍

Problem 5

Convert the decimal number 128 to hexadecimal.

Okay, lets begin

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.

Well explained 👍

FAQs on Decimal to Hexadecimal Conversion

1.What is the method to convert decimal to hexadecimal?

The conversion method involves dividing the decimal number by 16, recording the remainders, and reading these remainders in reverse order for the hexadecimal equivalent.

2.What is the hexadecimal equivalent of the decimal number 255?

The hexadecimal equivalent of the decimal number 255 is FF.

3.How do hexadecimal digits differ from decimal digits?

Hexadecimal digits include 0-9 and A-F, where A-F represent values 10-15. Decimal digits only include 0-9.

4.Why is hexadecimal used in computing?

Hexadecimal is used in computing because it provides a more compact and readable representation of binary-coded values, which is useful in programming and digital electronics.

5.How do you handle remainders when converting to hexadecimal?

Remainders are recorded at each division step, and the hexadecimal value is formed by reading these remainders in reverse order.

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.

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.