How to Convert Decimal to Hexadecimal Numbers (with Examples)
The concept of Decimal to Hex plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Learning how to convert decimal numbers (base-10) to hexadecimal (base-16) is especially helpful in competitive exams, computer science, and electronics.
What Is Decimal to Hex?
A Decimal to Hex conversion is the process of changing a number from the decimal system (which uses digits 0-9 and is based on powers of 10) to the hexadecimal system (which uses digits 0-9 and letters A-F, based on powers of 16). You’ll find this concept applied in areas such as base conversions, digital electronics, and coding/programming.
Key Formula for Decimal to Hex
Here’s the standard method:
Repeatedly divide the decimal number by 16. Each time, write down the remainder. The hexadecimal digits are the remainders read from last to first.
Cross-Disciplinary Usage
Decimal to hex 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, Olympiads, NTSE, and technical interviews will also see its relevance in many questions. In coding, hexadecimal numbers are often used to specify memory addresses, error codes, or color values.
Step-by-Step Illustration
Let’s learn how to convert a decimal number to hex using simple steps. Follow the division-remainder method:
- Pick your decimal number. (Example: 789)
- Divide the number by 16. Write the quotient and the remainder.
789 ÷ 16 = 49, remainder = 5 - Now, divide the quotient again by 16. Write the new quotient and remainder.
49 ÷ 16 = 3, remainder = 1 - Repeat until your quotient is 0. (Here: 3 ÷ 16 = 0, remainder = 3)
- The hex number is the remainders read from last to first.
So, 789 in decimal = 315hex
Note: If you get a remainder of 10-15, you write them as A-F (10 = A, 11 = B, ..., 15 = F).
Decimal to Hex Table (1 to 32)
| Decimal (Base 10) |
Hexadecimal (Base 16) |
Decimal | Hexadecimal |
|---|---|---|---|
| 0 | 0 | 17 | 11 |
| 1 | 1 | 18 | 12 |
| 2 | 2 | 19 | 13 |
| 3 | 3 | 20 | 14 |
| 4 | 4 | 21 | 15 |
| 5 | 5 | 22 | 16 |
| 6 | 6 | 23 | 17 |
| 7 | 7 | 24 | 18 |
| 8 | 8 | 25 | 19 |
| 9 | 9 | 26 | 1A |
| 10 | A | 27 | 1B |
| 11 | B | 28 | 1C |
| 12 | C | 29 | 1D |
| 13 | D | 30 | 1E |
| 14 | E | 31 | 1F |
| 15 | F | 32 | 20 |
| 16 | 10 |
Speed Trick or Vedic Shortcut
If you are in a hurry, remember this trick: For numbers less than 16, decimal to hex is the same (0-15 = 0-F). For larger numbers, divide and use the remainder system as shown above. Memorising common hex values using the table is a quick way to save time in exams and coding rounds. Vedantu live classes often highlight such speed strategies for students.
Decimal to Hex in Python, Excel, and JavaScript
Programming languages make this process even faster. Here’s how:
- Python:
hex(789)→ returns '0x315' - Excel:
=DEC2HEX(789)→ returns 315 - JavaScript:
(789).toString(16)→ returns '315'
Try These Yourself
- Convert 65 to hexadecimal.
- Find the hex value of 255.
- Change 108 to base-16.
- Reverse: What is the decimal value of 1A hex?
Frequent Errors and Misunderstandings
- Reading remainders in the wrong order (always write from last to first step!)
- Confusing values above 9: Remember 10=A, 11=B, ..., 15=F.
- Skipping quotient/remainder when zero or not dividing fully.
Relation to Other Concepts
The idea of Decimal to Hex connects closely with decimal to binary conversion and the hexadecimal number system. Mastering this helps with understanding conversions in computer science and digital logic circuits. You can practise other number systems, such as binary, octal, and more, through Vedantu resources.
Classroom Tip
A quick way to remember hex values is to make a small flashcard: 0-9 as usual, and then 10=A, 11=B, ..., 15=F. Practice with random numbers to strengthen your skills! Vedantu’s teachers use plenty of visuals and quizzes to make these conversions easy for you.
We explored Decimal to Hex—from definition, conversion steps, tricks, common errors, and deep links with other topics and programming uses. Keep practicing and use Vedantu’s stepwise solutions and topic tables to become a base conversion pro!
Internal Links to Related Topics
FAQs on Decimal to Hex Conversion: Methods, Table & Calculator
1. What is decimal to hex conversion in mathematics?
Decimal to hex conversion involves changing a number from base-10 (decimal) to base-16 (hexadecimal). It's essential for understanding computer systems, digital electronics, and various programming tasks. The hexadecimal system uses digits 0-9 and letters A-F (representing 10-15).
2. How do I convert a decimal number to its hexadecimal equivalent?
To convert a decimal number to hexadecimal, repeatedly divide the decimal number by 16. Record the remainders. The hexadecimal representation is the sequence of remainders, read from bottom to top. For example, converting 255 to hex: 255/16 = 15 R 15; 15/16 = 0 R 15. The remainders are 15 and 15, which are represented as 'F' and 'F' in hexadecimal. Thus, 255 (decimal) = FF (hexadecimal).
3. What is the hexadecimal representation of the decimal number 789?
To convert 789 to hexadecimal:
789 ÷ 16 = 49 remainder 5
49 ÷ 16 = 3 remainder 1
3 ÷ 16 = 0 remainder 3
Reading the remainders from bottom to top, we get 315. Therefore, 789 (decimal) is 315 (hexadecimal).
4. Why is hexadecimal used in computing?
Hexadecimal is used in computing because it provides a more compact representation of binary data than decimal. Each hexadecimal digit represents four binary digits (bits), making it easier to read and write binary data. It’s commonly used in programming, memory addressing, and color codes (e.g., #FF0000 for red).
5. Is there an easy way to convert decimal to hex without manual calculation?
Yes, there are online decimal-to-hexadecimal converters and calculators available. Many programming languages also have built-in functions for this conversion. These tools can save time and reduce the risk of errors during the conversion process.
6. How do I convert larger decimal numbers to hexadecimal?
The process remains the same for larger numbers: repeatedly divide by 16 and record the remainders. The remainders, written in reverse order, form the hexadecimal representation. Remember to convert remainders greater than 9 to their hexadecimal equivalents (A=10, B=11, C=12, D=13, E=14, F=15).
7. What are some common mistakes to avoid during decimal-to-hex conversion?
Common mistakes include incorrect remainders, forgetting to convert remainders above 9 to their hexadecimal letters, and incorrectly ordering the remainders (they should be read from bottom to top). Double-checking your work is key.
8. How is decimal-to-hex conversion used in programming?
In programming, hexadecimal is frequently used to represent colors, memory addresses, and other data. Conversion is needed when working with these data types. Many programming languages provide functions to handle this conversion efficiently.
9. Can I convert negative decimal numbers to hexadecimal?
Yes, you can convert negative decimal numbers to hexadecimal. The process is similar to converting positive numbers, but you need to consider the representation of negative numbers in the chosen system (e.g., two's complement). This might involve additional steps depending on your chosen method and representation of negative numbers.
10. How does decimal-to-hex conversion relate to other number systems (binary, octal)?
All these number systems (binary, octal, decimal, hexadecimal) represent the same values but use different bases. Conversion between them involves changing the base. Understanding these conversions is crucial in computer science and digital electronics. Hexadecimal provides a compact alternative for representing binary numbers, making it a bridge between binary and human-readable formats.
11. What is a decimal to hex conversion table, and how can it help?
A decimal to hex conversion table provides a quick reference for converting small decimal numbers (usually 0-255) directly to their hexadecimal equivalents. This table aids in faster conversions, especially during exams or quick calculations, eliminating the need for manual division.
