How to Convert Decimal to Hexadecimal With Examples
The concept of Hexadecimal Number System plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios.
What Is Hexadecimal Number System?
A Hexadecimal Number System is defined as a positional number system having a base of 16. It uses 16 symbols: numerals 0–9 and letters A–F, where A stands for 10, B for 11, C for 12, D for 13, E for 14, and F for 15 in decimal. You’ll find this concept applied in areas such as computer science (memory addresses, programming), digital electronics, and color coding in web design.
Key Features of the Hexadecimal Number System
- It is a base 16 system (positions are weighted by powers of 16)
- Digits used: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
- Letters represent values above 9: A = 10, B = 11, ..., F = 15
- Common in computer technology due to easy conversion with binary
- Compactly represents large numbers compared to decimal or binary
Hexadecimal Numbers Table (0 to 20)
| Decimal | Hexadecimal | Binary |
|---|---|---|
| 0 | 0 | 0000 |
| 1 | 1 | 0001 |
| 2 | 2 | 0010 |
| 3 | 3 | 0011 |
| 4 | 4 | 0100 |
| 5 | 5 | 0101 |
| 6 | 6 | 0110 |
| 7 | 7 | 0111 |
| 8 | 8 | 1000 |
| 9 | 9 | 1001 |
| 10 | A | 1010 |
| 11 | B | 1011 |
| 12 | C | 1100 |
| 13 | D | 1101 |
| 14 | E | 1110 |
| 15 | F | 1111 |
| 16 | 10 | 0001 0000 |
| 17 | 11 | 0001 0001 |
| 18 | 12 | 0001 0010 |
| 19 | 13 | 0001 0011 |
| 20 | 14 | 0001 0100 |
Hexadecimal vs Other Number Systems
| System | Base | Digits Used | Example: 16 |
|---|---|---|---|
| Decimal | 10 | 0-9 | 16 |
| Binary | 2 | 0, 1 | 10000 |
| Octal | 8 | 0-7 | 20 |
| Hexadecimal | 16 | 0-9, A-F | 10 |
How to Convert Decimal to Hexadecimal
Steps to convert a decimal number to hexadecimal:
1. Divide the decimal number by 16 and write down the remainder.2. Divide the quotient again by 16; write the new remainder.
3. Repeat until the quotient is 0.
4. The hexadecimal value is the string of remainders written in reverse order. Use A–F for remainders 10–15.
Example: Convert 24210 to hexadecimal.
1. 242 ÷ 16 = 15, remainder 22. 15 ÷ 16 = 0, remainder 15 (F)
3. Collect remainders from bottom: F2
So, 24210 = F216.
How to Convert Hexadecimal to Decimal
Multiply each hex digit by the power of 16 based on its position (rightmost = 160) and add them up.
Example: Convert AB416 to decimal.
1. A = 10, B = 11, 4 = 42. 10 × 162 = 2560
3. 11 × 161 = 176
4. 4 × 160 = 4
5. Add: 2560 + 176 + 4 = 274010
Step-by-Step Conversion: Binary to Hexadecimal
Group the binary number into blocks of 4 digits (from right). Convert each block to its hex equivalent.
Example: Convert 1100011111012 to hexadecimal.
1. Group: 1 1000 1111 101 (pad leftmost group: 0001 1000 1111 1101)2. 0001 = 1, 1000 = 8, 1111 = F, 1101 = D
3. Answer: 18FD16
Real-Life and Cross-Disciplinary Usage
The hexadecimal number system is not only useful in Maths but also plays an important role in Physics, Computer Science, and daily logical reasoning. Students preparing for exams like JEE or Olympiads will see its relevance in:
- HTML/CSS color codes (e.g., #FF5733 for orange)
- Memory addresses in computers (compact representation of bytes)
- Machine-level programming and debugging
- Storing binary data efficiently
Vedantu provides easy video explanations about connections between hexadecimal, binary, and decimal for both school and competitive exams.
Speed Trick or Common Shortcut
To convert a large binary to hex quickly, split binary into 4-bit blocks (right to left) and replace each with its hexadecimal equivalent using a chart. This reduces long calculations and avoids errors.
Example Trick: 1111 11012 → F D16
Tricks like these save time in board exams and are used in many Vedantu live doubt-sessions.
Try These Yourself
- Write the hexadecimal numbers from 1 to 16.
- Convert decimal 121 to hexadecimal.
- Convert 7B516 to decimal.
- What is the hex value for 1011012?
Frequent Errors and Misunderstandings
- Forgetting that after F, the next value is 10 (not G).
- Mixing up the position value (powers of 16 are critical).
- Confusing hexadecimal with octal (base 8) or decimal (base 10).
- Using the wrong binary group size (always 4 bits for hex).
Relation to Other Concepts
The idea of Hexadecimal Number System connects closely with topics such as the Binary Number System and the Decimal Number System. Mastering this topic helps with tasks like number system conversions, programming basics, and digital electronics circuits.
Classroom Tip
A quick way to remember hexadecimal letters is to use the mnemonic "A Big Cat Doesn't Eat Fish" for A-F (A=10, ..., F=15). Vedantu’s teachers highlight such patterns in live classes for easier recall.
We explored Hexadecimal Number System—from definition, chart, examples, conversion methods, errors, and connections to other number systems. Continue practicing with Vedantu to become confident in using this concept in both exams and real-life applications.
Useful Resources and Further Reading
FAQs on Hexadecimal Number System: Definition, Conversion & Uses
1. What is the hexadecimal number system?
The hexadecimal number system, also known as base-16, is a positional numeral system that uses 16 symbols to represent numbers. These symbols are 0-9 and the letters A-F, where A represents 10, B represents 11, and so on until F, which represents 15. It's commonly used in computer science and digital electronics for its compact representation of binary data.
2. How do you convert decimal to hexadecimal?
To convert a decimal number to hexadecimal, repeatedly divide the decimal number by 16. The remainders, read in reverse order, form the hexadecimal equivalent. Each remainder is represented by its corresponding hexadecimal digit (0-9 and A-F).
For example, to convert 255 to hexadecimal:
255 ÷ 16 = 15 remainder 15 (F)
15 ÷ 16 = 0 remainder 15 (F)
Reading the remainders in reverse order: FF. Therefore, (255)10 = (FF)16
3. How do you convert hexadecimal to decimal?
To convert a hexadecimal number to decimal, multiply each digit by the corresponding power of 16 (starting from the rightmost digit with 160, then 161, and so on) and sum the results. Remember to use the decimal equivalent for the letters A-F (A=10, B=11, ..., F=15). For example, (1A)16 = (1 × 161) + (10 × 160) = 16 + 10 = 2610
4. What are the advantages of using the hexadecimal number system?
Hexadecimal offers several advantages: It provides a more compact representation of binary data than decimal, making it easier to read and write large binary numbers. It also simplifies conversions between binary and other number systems. Hexadecimal is widely used in programming, memory addressing, and color codes (e.g., HTML color codes).
5. What are the applications of the hexadecimal number system?
Hexadecimal finds extensive use in various areas, including:
• Computer programming: Representing memory addresses, color codes in HTML and CSS, and data in various formats.
• Digital electronics: Representing machine code instructions, memory locations, and data registers.
• Data representation: Encoding and decoding data efficiently.
6. How is hexadecimal used in representing colors?
In HTML, CSS, and other web development contexts, colors are often specified using hexadecimal color codes. These codes consist of six hexadecimal digits (#RRGGBB), where RR represents the red component, GG the green component, and BB the blue component of the color. Each component ranges from 00 to FF (0-255 in decimal).
7. What is the difference between hexadecimal and binary number systems?
The key difference lies in their base: Hexadecimal uses base-16 (digits 0-9, A-F), while binary uses base-2 (digits 0 and 1). Hexadecimal provides a more concise way to represent binary data because each hexadecimal digit corresponds to four binary digits (a nibble).
8. What is the difference between hexadecimal and decimal number systems?
Decimal uses base-10 (digits 0-9), while hexadecimal uses base-16 (digits 0-9, A-F). The main difference lies in the number of symbols used and the way they represent numerical values. Larger numbers are expressed more compactly using hexadecimal compared to decimal.
9. How do you add hexadecimal numbers?
Adding hexadecimal numbers is similar to adding decimal numbers, but you carry over when the sum exceeds 15 (F). Remember that A=10, B=11, C=12, D=13, E=14, and F=15. For example, adding 2A and 3B:
2A
+3B
-----
65 (2A + 3B = 65 in hexadecimal)
10. How do you subtract hexadecimal numbers?
Subtracting hexadecimal numbers involves borrowing when a digit in the minuend is smaller than the corresponding digit in the subtrahend. Remember the decimal equivalents of A-F (A=10, B=11, ..., F=15). Borrowing from the next higher place value involves adding 16 to the digit in the lower place value.
11. Can negative numbers be represented in hexadecimal?
Yes, negative numbers can be represented in hexadecimal using techniques like two's complement representation, which is commonly employed in computer systems. This involves taking the binary complement of the positive representation and adding 1.
12. What happens after F in hexadecimal?
After F (15), the next number in hexadecimal is 10, which represents 16 in decimal. This is analogous to how decimal increments from 9 to 10.
