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Last updated on 15 September 2025
A hexadecimal number system is a type of number system, with a base of 16. It includes numbers from 0 to 9 and letters A to F. 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.
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. They are used for performing calculations, representing data, and processing information efficiently.
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 represents 10, B represents 11, and so on. Similar to the decimal system (base 10), hexadecimal counts up to F instead of stopping at 9. Each digit in hexadecimal has a weight of 16ⁿ, where n represents its position.
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 |
In the hexadecimal number system (base 16), each digit's place value is determined by powers of 16 (16⁰, 16¹, 16², ...), 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 × 162 + F × 161 + 3 × 160 = 2 × 256 + 15 × 16 + 3 × 1 = 755 in decimal.
Across fields, a hexadecimal number system is used. Let us explore how the hexadecimal number system is used in different areas:
Students often make mistakes when learning the hexadecimal system. Here are common mistakes and tips to avoid them
Convert 1A₁₆ to its decimal equivalent.
1A₁₆ = 26₁₀
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
Convert 2F₁₆ to decimal.
2F₁₆ = 47₁₀
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.
Convert 255₁₀ into hexadecimal.
255₁₀ = FF₁₆
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).
Reading the remainders in reverse order gives the hex digits: F and F.
Convert 1000₁₀ to hexadecimal.
1000₁₀ = 3E8₁₆
Divide 1000 by 16:
1000 ÷ 16 = 62 with remainder
Divide the quotient 62 by 16:
62 ÷ 16 = 3 remainder 14 (E in hex).
Divide the quotient 3 by 16:
3 ÷ 16 = 0 with remainder of 3
Write the remainders in reverse order:
3, E, 8
Compute C8₁₆ ÷ 4₁₆.
C8₁₆ ÷ 4₁₆ = 32₁₆
Convert C8 to decimal: C = 12 → 12 × 16 + 8 = 200₁₀.
Convert 4₁₆ to decimal: 4₁₀.
Divide: 200 ÷ 4 = 50.
Convert 50 back to hex: 50 ÷ 16 = 3 remainder 2 → 32₁
⇒ C8₁₆ ÷ 4₁₆ = 32₁₆
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.
: She loves to read number jokes and games.