HEX HeroConvert Hex to Denary
Enter your hexadecimal values below—one per line—and get instant denary conversions. Whether you're preparing for GCSE Computer Science exams, checking homework answers, or practicing number base conversions, this tool makes hex-to-denary calculations quick and accurate.
How to convert Hexadecimal to Denary - a step by step tutorial
GCSE-focused guide with worked examples. Master place value multiplication, converting A-F letters to numbers, and checking your answers with reverse conversion.
Conversion Steps
Converting hexadecimal (base-16) to denary (base-10) is straightforward once you understand place values. Perfect for GCSE and A-Level students!
Write Place Values
Each hex digit position represents a power of 16. Rightmost is 160 (=1), next is 161 (=16), then 162 (=256), and so on.
Example: For 2F, positions are 16¹ and 16⁰
Convert Letters to Numbers
Replace hex letters with their denary values: A=10, B=11, C=12, D=13, E=14, F=15. Leave numeric digits as they are.
Example: F becomes 15, so 2F = 2 and 15
Multiply by Powers
Multiply each digit by its place value (power of 16). Start from the right with 160.
Example: (2 × 16) + (15 × 1) = 32 + 15
Add Everything Together
Sum all the products from step 3. The total is your denary answer!
Example: 32 + 15 = 47 (denary)
Worked Example: Converting A5 to Denary
Let's work through a complete conversion with clear steps for exam preparation:
Given: A5 (hexadecimal)
We need to convert this to denary (base-10)
A is in 161 position (worth 16 each)
5 is in 160 position (worth 1 each)
A = 10 (in denary)
5 = 5 (stays the same)
10 × 16 = 160
5 × 1 = 5
160 + 5 = 165
A5 hexadecimal = 165 denary ✓
Hex to Denary Quick Reference for Students
Common hexadecimal values you'll encounter in GCSE Computer Science. Learn these to speed up exam questions!
| Hexadecimal | Denary | Study Tip |
|---|---|---|
| F | 15 | Largest single hex digit, memorize this! |
| 10 | 16 | One more than F, starts two-digit hex numbers |
| 1F | 31 | (1 × 16) + (15 × 1) = 16 + 15 |
| 20 | 32 | 2 × 16 = 32, common in exams |
| 64 | 100 | (6 × 16) + (4 × 1) = 96 + 4 |
| FF | 255 | Maximum byte, RGB max, very important! |
| 100 | 256 | (1 × 256) + (0 × 16) + (0 × 1) |
| 3E8 | 1000 | (3 × 256) + (14 × 16) + (8 × 1) |
Understanding Hexadecimal Place Values
Just like denary (base-10) uses powers of 10, hexadecimal uses powers of 16. This concept is fundamental for UK GCSE Computer Science!
Place Value Chart
| Position | 16³ | 16² | 16¹ | 16⁰ |
|---|---|---|---|---|
| Worth: | 4096 | 256 | 16 | 1 |
| Example: 2A3F | 2 | A (10) | 3 | F (15) |
| Calculate: | 2 × 4096 | 10 × 256 | 3 × 16 | 15 × 1 |
| Result: | 8192 | 2560 | 48 | 15 |
Total: 8192 + 2560 + 48 + 15 = 10815 denary
Test Your Knowledge: Hex to Denary Practice
Try these exam-style questions by hand before checking your answers. Show all working for maximum marks!
Foundation Questions
- 1.Convert A (hex) to denary
- 2.Convert 1F (hex) to denary
- 3.Convert 2E (hex) to denary
Show Working & Answers
1. A = 10 (single digit, no calculation needed)
2. 1F = (1 × 16) + (15 × 1) = 16 + 15 = 31
3. 2E = (2 × 16) + (14 × 1) = 32 + 14 = 46
Intermediate Questions
- 4.Convert 3C (hex) to denary
- 5.Convert C8 (hex) to denary
- 6.Convert AB (hex) to denary
Show Working & Answers
4. 3C = (3 × 16) + (12 × 1) = 48 + 12 = 60
5. C8 = (12 × 16) + (8 × 1) = 192 + 8 = 200
6. AB = (10 × 16) + (11 × 1) = 160 + 11 = 171
Advanced Questions
- 7.Convert 1A4 (hex) to denary
- 8.Convert FFF (hex) to denary
- 9.Convert 800 (hex) to denary
Show Working & Answers
7. 1A4 = (1 × 256) + (10 × 16) + (4 × 1) = 256 + 160 + 4 = 420
8. FFF = (15 × 256) + (15 × 16) + (15 × 1) = 3840 + 240 + 15 = 4095
9. 800 = (8 × 256) + (0 × 16) + (0 × 1) = 2048
Challenge Questions
- 10.Convert DEAD (hex) to denary
- 11.What is 100 hex in denary?
- 12.Convert CAFE (hex) to denary
Show Working & Answers
10. DEAD = (13 × 4096) + (14 × 256) + (10 × 16) + (13 × 1) = 57005
11. 100 = (1 × 256) + (0 × 16) + (0 × 1) = 256
12. CAFE = (12 × 4096) + (10 × 256) + (15 × 16) + (14 × 1) = 51966
Why "Denary" Instead of "Decimal"?
If you're studying in the UK, you'll see "denary" throughout your GCSE and A-Level Computer Science courses. It's the British English term for the decimal (base-10) number system we use daily.
📚 UK Exam Boards Use "Denary"
AQA, OCR, Edexcel, and WJEC all use "denary" in their specifications. Using this term in your exam answers shows familiarity with the correct terminology and can help you score higher marks in extended responses.
🌍 International vs UK English
"Decimal" is the international term, widely used in American textbooks and programming. Both mean exactly the same thing: base-10 numbering with digits 0-9. Your exam will accept either, but "denary" is more precise for UK contexts.
⚠️ Common GCSE Mistakes to Avoid
❌ Forgetting to Convert Letters
Wrong: A5 = (A × 16) + (5 × 1) — You can't multiply by the letter A!
Right: Convert A to 10 first, then (10 × 16) + (5 × 1) = 165
❌ Wrong Place Values
Wrong: Using powers of 10 instead of 16 (e.g., 2F = 2 × 10 + 15)
Right: Always use powers of 16! 2F = (2 × 16) + (15 × 1) = 47
❌ Miscounting Positions
Wrong: Treating the leftmost digit as 16⁰ instead of starting from the right
Right: ALWAYS start counting positions from the right. Rightmost = 16⁰, next = 16¹, etc.
❌ Mixing Up Letter Values
Wrong: D = 12 or E = 13 (common confusion with C and D)
Right: C=12, D=13, E=14, F=15. Write the reference on your exam paper!
Student FAQs: Hex to Denary Conversion
Is denary the same as decimal?
Yes! "Denary" and "decimal" are exactly the same thing—both mean base-10. UK exam boards (AQA, OCR, Edexcel) prefer "denary," while international sources often use "decimal." You can use either term in your exams, but sticking to "denary" shows you understand UK specifications.
Do I need to memorize the letter values?
Absolutely! You must know A=10, B=11, C=12, D=13, E=14, F=15 by heart. These appear in every hex conversion question. Make flashcards, practice daily, or use mnemonics. Most exams allow you to write a reference at the top of your answer sheet—do this immediately!
What's the easiest way to remember powers of 16?
Remember: 16⁰ = 1, 16¹ = 16, 16² = 256, 16³ = 4096. Each one is 16 times the previous. For two-digit hex, you only need 16 and 1. For three-digit, add 256. Practice with the same examples repeatedly until it's automatic!
Can I use a calculator in GCSE for this?
Calculators are typically allowed, but you MUST show full working. Use the calculator to check multiplication and addition, but write every step clearly: "(10 × 16) + (5 × 1) = 160 + 5 = 165." Examiners need to see your method to award marks.
Why is FF always 255?
FF is the maximum value in a byte (8 bits). Converting: FF = (15 × 16) + (15 × 1) = 240 + 15 = 255. This is why RGB colors range from 00 to FF—each color channel uses one byte (0-255). Knowing this helps with web design and graphics coursework!
How do I check if my answer is correct?
Convert back! Take your denary answer and convert it to hex using the division method. If you get the original hex value, you're correct. This reverse-check catches mistakes and demonstrates strong understanding to examiners—worth including if you have extra time in the exam!
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