Decimal to Hexadecimal Conversion

Decimal to hexadecimal is a system of conversion that is often used in computers and digital systems. The decimal number system has a base of 10. It has only 10 notations, i.e., 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Whereas the hexadecimal system operates with a base of 16 because there are a total of 16 notations in it: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and A, B, C, D, E, F. To denote the double digits 10, 11, 12, 13, 14, 15 in the hexadecimal number system, we use characters A, B, C, D, E, F respectively. Let us learn more about the conversion methods of decimal to hexadecimal and the steps of conversion associated with it.

Decimal

A decimal number is a number expressed in the base 10 numeral system. Decimal numbers' digits have 10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Each digit of a decimal number counts a power of 10.

Decimal number example:

653₁₀ = 6×10² + 5×10¹ + 3×10⁰

Hexadecimal

A hexadecimal number is a number expressed in the base 16 numeral system. Hexadecimal numbers' digits have 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Each digit of a hexadecimal number counts a power of 16.

Hexadecimal number example:

62C₁₆ = 6×16² + 2×16¹ + 12×16⁰ = 1580₁₀

How to Convert from Decimal to Hexadecimal

Conversion steps:

Divide the number by 16.
Get the integer quotient for the next iteration.
Get the remainder for the hex digit.
Repeat the steps until the quotient is equal to 0.

Example

Understanding Decimal-to-Hexadecimal Conversion

Decimal-to-hexadecimal conversion involves converting decimal numbers (base 10) into their corresponding hexadecimal representations (base 16). Hexadecimal uses digits 0-9 and letters A-F to represent values from 0 to 15, respectively.

The general approach to converting decimal numbers to hexadecimal includes:

Divide the decimal number by 16 and record the remainder.
Repeat the division until the quotient is 0.
Write the remainders in reverse order to get the hexadecimal representation.

Steps for Decimal-to-Hexadecimal Conversion

Step 1: Divide the decimal number by 16, noting the quotient and remainder.

Step 2: Repeat the division until the quotient is 0.

Step 3: Write the remainders in reverse order to obtain the hexadecimal number.

Example: Converting Decimal to Hexadecimal

Convert \( 254 \) to hexadecimal:

Step 1: Divide \( 254 \) by \( 16 \): quotient \( 15 \), remainder \( 14 \) (which is \( E \) in hexadecimal).
Step 2: Divide \( 15 \) by \( 16 \): quotient \( 0 \), remainder \( 15 \) (which is \( F \) in hexadecimal).
Write the remainders in reverse order: \( FE \).
Final hexadecimal result: \( FE \).

Conversion Table for Quick Reference

Here is a quick reference for some decimal numbers and their hexadecimal equivalents:

0 → 0
1 → 1
2 → 2
5 → 5
10 → A
15 → F
16 → 10
65 → 41
255 → FF

Applications of Decimal-to-Hexadecimal Conversion

Decimal-to-hexadecimal conversion is commonly used in:

Encoding numerical data for memory addresses, color codes in web design, and machine-level programming.
Representing large numbers more compactly in programming and digital systems.
Working with low-level computing tasks and understanding how data is represented in memory.

Practice Problem

Convert \( 103 \) to hexadecimal:

Solution:
- Step 1: Divide \( 103 \) by \( 16 \): quotient \( 6 \), remainder \( 7 \).
- Step 2: Divide \( 6 \) by \( 16 \): quotient \( 0 \), remainder \( 6 \).
Write the remainders in reverse order: \( 67 \).
Final hexadecimal result: \( 67 \).

Decimal-to-Hexadecimal Conversion Examples Table
Problem Type	Description	Steps to Solve	Example
Basic Conversion	Converting a decimal number to its hexadecimal equivalent.	Divide the decimal number by 16. Record the remainder (which will be a digit in hexadecimal, 0-9 or A-F). Repeat the process with the quotient until the quotient is 0. Write the remainders in reverse order to get the hexadecimal result.	For \( 72 \): Divide by 16: \( 72 \div 16 = 4 \) remainder \( 8 \). Divide by 16: \( 4 \div 16 = 0 \) remainder \( 4 \). Hexadecimal: \( 48 \).
Handling Larger Numbers	Converting larger decimal numbers to hexadecimal.	Follow the same division-by-16 method, recording each remainder. Write the remainders in reverse order.	For \( 255 \): Divide by 16: \( 255 \div 16 = 15 \) remainder \( 15 \) (F). Divide by 16: \( 15 \div 16 = 0 \) remainder \( 15 \) (F). Hexadecimal: \( FF \).
Verifying Conversion	Checking the accuracy of decimal-to-hexadecimal conversion.	Convert the hexadecimal number back to decimal. Ensure the decimal result matches the original number.	For \( 48 \) (hexadecimal for \( 72 \)): Hexadecimal: \( 48 \). Convert back to decimal: \( 4 \times 16^1 + 8 \times 16^0 = 72 \). Decimal: \( 72 \), matches the original input.
Handling Special Cases	Converting special decimal numbers to hexadecimal (e.g., powers of 16).	For powers of 16, the hexadecimal representation will have one digit and powers of 16.	For \( 256 \): Decimal: \( 256 \). Hexadecimal: \( 100 \).
Applications	Understanding where decimal-to-hexadecimal conversion is used.	Hexadecimal representation is commonly used in computer science for memory addresses, color codes (e.g., in HTML), and data storage. Used in programming, cryptography, and networking to simplify binary representations.	Example: Converting decimal numbers to hexadecimal for memory addressing in computing systems.