HEX HeroConvert Denary to Hex
Enter your denary numbers below—one per line—and get instant hexadecimal conversions. Whether you're studying for GCSE Computer Science exams, working through coursework, or practicing number system conversions, this tool helps you master base-16 notation.
How to convert Denary to Hexadecimal - a step by step tutorial
Perfect for GCSE Computer Science students. Work through exam-style examples, learn the division algorithm, and ace your number system conversion questions.
Step-by-Step Instructions
Converting from denary (base-10) to hexadecimal (base-16) is a key skill in GCSE Computer Science and A-Level Computing. Follow these clear steps:
Divide by 16
Take your denary number and divide it by 16. Write down the quotient (whole number result) and keep track of the remainder.
Example: 157 ÷ 16 = 9 remainder 13
Convert Remainder
If the remainder is 0-9, write it as is. If it's 10-15, convert to hex letters: 10=A, 11=B, 12=C, 13=D, 14=E, 15=F.
Example: Remainder 13 becomes D
Repeat Division
Take the quotient from step 1 and divide by 16 again. Keep repeating until your quotient becomes 0.
Example: 9 ÷ 16 = 0 remainder 9
Read Upwards
Write your remainders from bottom to top (last remainder first). This gives you the hexadecimal answer.
Example: 157 in denary = 9D in hex
Worked Example: Converting 250 to Hexadecimal
Let's work through a complete example step-by-step, perfect for GCSE exam practice:
Check your work: FA in hex = (15 × 16) + (10 × 1) = 240 + 10 = 250 ✓
Common Denary to Hex Conversions for GCSE
These frequently appear in GCSE Computer Science exams and coursework. Memorizing these can save valuable time!
| Denary | Hexadecimal | Why It's Important |
|---|---|---|
| 0 | 0 | Starting point, represents zero value |
| 15 | F | Largest single hex digit (1111 in binary) |
| 16 | 10 | First two-digit hex number (base value) |
| 100 | 64 | Common exam question benchmark |
| 255 | FF | Maximum 8-bit value, RGB color channel max |
| 256 | 100 | One more than FF, important boundary |
| 512 | 200 | Powers of 2 conversion practice |
| 1000 | 3E8 | Round number, tests understanding of place values |
What is Denary and Why Use Hexadecimal?
Denary is the British English term for the decimal number system (base-10) that we use every day. It's called "denary" because it uses ten digits (0-9), derived from the Latin word decem meaning ten. In UK schools, especially for GCSE and A-Level Computer Science, you'll see "denary" rather than "decimal."
Hexadecimal (base-16) uses sixteen digits: 0-9 and A-F. Computers use hexadecimal because it efficiently represents binary data—each hex digit corresponds to exactly 4 binary bits, making it easier for programmers and students to work with computer memory and code.
🎓 Why Learn This for GCSE?
Number system conversions are essential in GCSE Computer Science (AQA, OCR, Edexcel). You'll encounter questions asking you to convert between denary, binary, and hexadecimal. Understanding hex helps you grasp how computers store colors, memory addresses, and error codes.
💡 Real-World Applications
Web designers use hex for colors (#FF5733 for orange-red). Game developers use hex for memory editing. Network engineers use hex for MAC addresses. Learning denary-to-hex conversion opens doors to understanding how digital technology really works!
Practice Questions for Students
Test your understanding with these exam-style questions. Try solving them by hand before using the converter!
Easy Level
- 1.Convert 10 (denary) to hexadecimal
- 2.Convert 25 (denary) to hexadecimal
- 3.Convert 64 (denary) to hexadecimal
Show Answers
1. A | 2. 19 | 3. 40
Medium Level
- 4.Convert 128 (denary) to hexadecimal
- 5.Convert 200 (denary) to hexadecimal
- 6.Convert 500 (denary) to hexadecimal
Show Answers
4. 80 | 5. C8 | 6. 1F4
Hard Level
- 7.Convert 999 (denary) to hexadecimal
- 8.Convert 2048 (denary) to hexadecimal
- 9.Convert 4095 (denary) to hexadecimal
Show Answers
7. 3E7 | 8. 800 | 9. FFF
Challenge Level
- 10.Convert 16777215 (denary) to hex (RGB white)
- 11.What denary number gives hex 100?
- 12.Why is FF important in colors?
Show Answers
10. FFFFFF | 11. 256 | 12. FF = 255 (max RGB channel)
Why Students Use This Denary to Hex Converter
Homework Help
Quickly check your manual conversions for GCSE homework. Perfect for verifying answers before submission and understanding where you made mistakes.
Exam Preparation
Practice with random numbers and build confidence. Use the converter to generate test cases and verify your working during revision sessions.
Web Design Projects
Convert RGB color values (0-255) to hex codes for CSS. Essential for creating custom colors in web development coursework and personal projects.
Programming Coursework
Understand memory addresses and error codes when learning Python, JavaScript, or other languages in Computing lessons.
Quick Reference
Instantly convert numbers during class or while reading technical documentation. No need to interrupt your learning flow with manual calculations.
Understanding Patterns
Experiment with different numbers to spot patterns. See how powers of 2 convert cleanly and why hex is more efficient than denary for computers.
GCSE Exam Tips: Denary to Hex Conversion
✏️ Show Your Working
Even if you know the answer, write out the division steps. Examiners award marks for method, not just the final answer. If you make a small arithmetic error but show correct method, you'll still earn partial marks.
🔤 Remember A-F Conversions
Quickly memorize: A=10, B=11, C=12, D=13, E=14, F=15. Write this reference at the top of your exam page if allowed. Many students lose marks by forgetting D=13 or E=14.
⬆️ Read Remainders Upwards
The most common mistake is writing remainders in the wrong order. Always read from bottom to top (last remainder becomes first hex digit). Draw an arrow to remind yourself!
✅ Check Your Answer
If time permits, convert your hex answer back to denary. Multiply each hex digit by its power of 16 and sum them. If you get your original number, you're correct!
📊 Know Common Values
Memorize: 15=F, 16=10, 255=FF, 256=100. These appear frequently in exams. Recognizing them instantly saves precious time and reduces errors.
Common Student Questions About Denary to Hex
What's the difference between denary and decimal?
There's no difference—they're the same thing! "Decimal" is the American/international term, while "denary" is preferred in UK schools and exam boards like AQA, OCR, and Edexcel. Both mean base-10 (the number system using digits 0-9).
Why do we learn hexadecimal in Computer Science?
Hexadecimal is essential because it represents binary data efficiently. Each hex digit equals 4 binary bits, making it easier to read memory addresses, color codes, and machine code. For example, binary 11111111 is just FF in hex—much shorter and clearer!
How do I remember which letters mean which numbers?
Think alphabetically: A is the 1st letter so A=10 (the first number after 9), B is 2nd so B=11, C is 3rd so C=12, and so on up to F=15. Practice with flashcards or write them out repeatedly until they're automatic.
What if I get a remainder bigger than 15?
That's impossible when dividing by 16! A remainder is always smaller than the divisor. The largest remainder you can get when dividing by 16 is 15 (which becomes F). If you got a bigger remainder, check your division working.
Can I use a calculator for the division?
In most GCSE exams, calculators are allowed, BUT you must show clear working. Use the calculator to check your division, but write out each step: "250 ÷ 16 = 15 remainder 10." Don't just write the final hex answer without showing the method!
Why is 255 denary equal to FF in hexadecimal?
255 is the maximum value you can store in 8 bits (one byte). Converting: 255 ÷ 16 = 15 remainder 15. Both remainders are 15, which is F in hex, giving us FF. This is why RGB colors range from 00 to FF (0 to 255)!
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