120 LearnersLast updated on July 23rd, 2025
Hexadecimal Number System
A hexadecimal number system is a type of number system, with a base of 16. It includes numbers from 0 to 9 and A to F from letters. Hexadecimal is considered one of the most convenient ways to use binary numbers in computers, and this is often done using a conversion table. Let us learn more about the hexadecimal number system in the topic given below.
What is a Number System?
A number system is a system for expressing numbers, it's a mathematical notation for representing numbers of a given set, using digits or other symbols. It defines a set of symbols (digits) and rules for their arrangement to form numerical values. The most common number systems include decimal (base 10), binary (base 2), octal (base 8), and hexadecimal (base 16). Number systems are fundamental in mathematics, computing, and digital electronics for performing calculations, data representation, and processing information efficiently.
What is a Hexadecimal Number System?
The word hexadecimal comes from Greek: "hex" means 6 and "deka" means 10. It uses 16 digits: 0 to 9 and A to F, where A stands for 10, B for 11, and so on. Similar to the regular decimal system (base 10), it counts up to F instead of stopping at 9. Each digit in hexadecimal has a weight 16 times greater than the previous one, following a positional number system.
Hexadecimal Numbers Conversions
The table below shows the hexadecimal to decimal conversions:
| Hexadecimal |
Decimal |
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 8 |
| 9 | 9 |
| A | 10 |
| B | 11 |
| C | 12 |
| D | 13 |
| E | 14 |
| F | 15 |
Place Value of Digits in Hexadecimal Number System
In the hexadecimal number system (base 16), each digit's place value is determined by powers of 16, similar to how the decimal system uses powers of 10. The rightmost digit represents 160 (ones place), the next represents 161 (sixteens place), followed by
162 (256’s place), and so on. Hexadecimal uses 16 symbols (0–9 and A–F), where A = 10, B = 11, ..., F = 15 in decimal. For example, in 2F3 (hex), the place values are: 2 x 162 + F x 161 + 3 x 160 = 2 x 256 + 15 x 16 + 3 x 1 = 755 in decimal.
Real Life Applications of Hexadecimal Number System
Across fields, a hexadecimal number system is used. Let us explore how the hexadecimal number system is used in different areas:
Computer Memory Addressing: For memory addressing, hexadecimal systems are used. Usually, binary form is used in storing data in computers. Too long binary numbers can crash the system, so the hexadecimal number system provides a more compact and concise format. System administrators can easily modify and locate these memory locations.
Color Representation in Digital Graphics: Hexadecimal is commonly used in digital graphics and web development for color representation. Colors on digital screens are defined by red, green, and blue (RGB) values, each ranging from 0 to 255. These values are used in hexadecimal to create a six-digit code, where the first two digits are red, the next two green, and the last two blue. This method simplifies color management in web design and digital imaging.
MAC Addresses in Networking:Every device that connects to a network has a unique identifier known as a MAC (Media Access Control) address, which is represented in hexadecimal format. A MAC address consists of six pairs of hexadecimal digits separated by colons or hyphens, such as 00:1A:2B:3C:4D:5E. This format makes it easier for network administrators to identify and manage devices on a network. It improves communication security and troubleshooting network issues.
Common Mistakes and How To Avoid Them in Hexadecimal Number System
Students tend to make mistakes while learning the hexadecimal number system. Let us see some common mistakes and how to avoid them:
Mistake 1
Confusing Hexadecimal Digits with Decimal Numbers
Remember that hexadecimal uses 16 symbols: 0–9 and A–F. When converting hex to decimal, always replace A = 10, B = 11, C = 12, D = 13, E = 14, F = 15 before performing calculations.
Mistake 2
Wrong Conversion from Hex to Decimal or Decimal to Hex
Use the positional method when converting. Multiply each hex digit by 16 raised to its positional power. Add all the values to get the decimal equivalent. Double-check your calculations or use a conversion tool if unsure.
Mistake 3
Ignoring Case Sensitivity in Programming
Always check the syntax rules of the programming language you are using. Stick to one convention (uppercase or lowercase) to avoid confusion.
Mistake 4
Forgetting the “0x” Prefix in Programming
Always use the correct notation when writing hex values in code:
C, C++, Java, Python: 0xFF
HTML/CSS Colors: #FF5733 (No "#0x" needed)
Mistake 5
Misinterpreting Hexadecimal Addition and Subtraction
Convert hex digits to decimal before performing arithmetic operations. If needed, perform the calculations in decimal and convert back to hexadecimal.
Solved Examples on Hexadecimal Number System
Problem 1
Convert 1A₁₆ to its decimal equivalent.
1A₁₆ = 26₁₀
Explanation
Write the hex digits with their positions (rightmost digit is position 0):
1 at position 1, A at position 0 (remember A = 10).
Multiply each digit by 16 raised to its position:
1 × 161 = 1 × 16 = 16
10 × 160 = 10 × 1 = 10
Sum the results:
16 + 10 = 26
Problem 2
Convert 2F₁₆ to decimal.
2F₁₆ = 47₁₀
Explanation
Identify the digits: 2 at position 1 and F at position 0 (F = 15).
Multiply each digit by 16 raised to its position:
2 × 161 = 2 × 16 = 32
15 × 160 = 15 × 1 = 15
Add the products:
32 + 15 = 47.
Problem 3
Convert 255₁₀ into hexadecimal.
255₁₀ = FF₁₆
Explanation
Divide 255 by 16:
255 ÷ 16 = 15 with a remainder of 15 (15 in hex is F).
Next, divide the quotient (15) by 16:
15 ÷ 16 = 0 with remainder
15 (again, F).
Read remainders in reverse order:
The hex digits are F and F.
Problem 4
Convert 1000₁₀ to hexadecimal.
1000₁₀ = 3E8₁₆
Explanation
Divide 1000 by 16:
1000 ÷ 16 = 62 with remainder
Divide the quotient 62 by 16:
62 ÷ 16 = 3 with remainder
14 (14 = E).
Divide the quotient 3 by 16:
3 ÷ 16 = 0 with remainder of 3
Write the remainders in reverse order:
3, E, 8
Problem 5
Compute C8₁₆ ÷ 4₁₆.
C8₁₆ ÷ 4₁₆ = 32₁₆
Explanation
Convert C8 to decimal:
C = 12, so C816 = 12 × 16 + 8 = 192 + 8 = 20010.
Convert 416 to decimal: 416 = 4₁₀
Divide: 200 ÷ 4 = 50
Convert 50 back to hexadecimal:
50 ÷ 16 = 3 remainder 2 (because 3 × 16 = 48, 50 − 48 = 2).
The hex is 32.
FAQs on Hexadecimal Number System
1.What is the hexadecimal number system?
2.How many digits are in the hexadecimal system?
3.What symbols are used in hexadecimal?
4.How do you convert a decimal number to hexadecimal?
5.Why is hexadecimal used in computing?
6.How can children in United Kingdom use numbers in everyday life to understand Hexadecimal Number System?
7.What are some fun ways kids in United Kingdom can practice Hexadecimal Number System with numbers?
8.What role do numbers and Hexadecimal Number System play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Hexadecimal Number System skills?
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
