Denary to Hexadecimal Converter
Convert denary (decimal, base 10) numbers to hexadecimal (base 16) format instantly. Hexadecimal uses digits 0-9 and letters A-F to represent values, making it popular in computing for memory addresses, colour codes, and data representation.
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Denary to Hexadecimal Conversion Table
Here’s a reference table showing common denary values and their hexadecimal equivalents. This is particularly useful for programmers and computer science students.
| Denary (Base 10) | Hexadecimal (Base 16) | Denary (Base 10) | Hexadecimal (Base 16) |
|---|---|---|---|
| 0 | 0 | 16 | 10 |
| 1 | 1 | 32 | 20 |
| 2 | 2 | 64 | 40 |
| 3 | 3 | 128 | 80 |
| 4 | 4 | 255 | FF |
| 5 | 5 | 256 | 100 |
| 6 | 6 | 512 | 200 |
| 7 | 7 | 1000 | 3E8 |
| 8 | 8 | 1024 | 400 |
| 9 | 9 | 2048 | 800 |
| 10 | A | 4096 | 1000 |
| 11 | B | 8192 | 2000 |
| 12 | C | 16384 | 4000 |
| 13 | D | 32768 | 8000 |
| 14 | E | 65535 | FFFF |
| 15 | F | 1048576 | 100000 |
Hexadecimal Digit Values
Hexadecimal uses 16 distinct symbols. The first ten are identical to denary (0-9), whilst the letters A through F represent values ten through fifteen.
Conversion Method and Steps
Division-Remainder Method
The most straightforward way to convert denary to hexadecimal involves repeated division by 16. This method works for any positive whole number and is commonly taught in GCSE Computer Science.
- Divide your denary number by 16
- Record the quotient (result) and the remainder
- If the remainder is 10-15, convert it to its hexadecimal letter (A-F)
- Divide the quotient by 16 again
- Repeat steps 2-4 until your quotient reaches 0
- Write all remainders in reverse order (bottom to top)
Worked Example 1: Convert 157 to Hexadecimal
Step 1: 157 ÷ 16 = 9 remainder 13 (D in hex)
Step 2: 9 ÷ 16 = 0 remainder 9
Result: Reading from bottom to top: 9D
So 157 in denary equals 9D in hexadecimal.
Worked Example 2: Convert 2019 to Hexadecimal
Step 1: 2019 ÷ 16 = 126 remainder 3
Step 2: 126 ÷ 16 = 7 remainder 14 (E in hex)
Step 3: 7 ÷ 16 = 0 remainder 7
Result: Reading from bottom to top: 7E3
So 2019 in denary equals 7E3 in hexadecimal.
Worked Example 3: Convert 255 to Hexadecimal
Step 1: 255 ÷ 16 = 15 remainder 15 (F in hex)
Step 2: 15 ÷ 16 = 0 remainder 15 (F in hex)
Result: Reading from bottom to top: FF
255 is the maximum value that can be represented by two hexadecimal digits, commonly used for RGB colour values.
Where Hexadecimal Gets Used
Web Colours
When you specify colours in CSS or HTML, you’re using hexadecimal. The code #FF5733 represents red (FF), green (57), and blue (33) values. Each pair is a hexadecimal number from 00 to FF (0 to 255 in denary).
Memory Addresses
Computer programmers use hexadecimal to reference memory locations. Instead of writing long binary addresses, hex provides a compact format. The address 0x7FFF represents a specific location in memory.
MAC Addresses
Every network card has a unique MAC address written in hexadecimal, like 00:1A:2B:3C:4D:5E. This identifies devices on networks.
Character Encoding
Unicode characters are often referenced by their hex code point. The pound sign (£) is U+00A3 in Unicode, where A3 is hexadecimal for 163.
Assembly Language
Low-level programming frequently uses hex values to represent opcodes and memory addresses because they’re more readable than binary but closer to how computers actually work.
Number System Conversions
Here’s how denary, binary, and hexadecimal relate to each other for the same values.
| Denary | Binary | Hexadecimal | Notes |
|---|---|---|---|
| 0 | 0000 | 0 | Minimum 4-bit value |
| 8 | 1000 | 8 | One byte half-value |
| 15 | 1111 | F | Maximum single hex digit |
| 16 | 10000 | 10 | Base of hexadecimal |
| 255 | 11111111 | FF | Maximum byte value |
| 256 | 100000000 | 100 | One byte plus one |
| 4096 | 1000000000000 | 1000 | 4 kilobytes |
| 65535 | 1111111111111111 | FFFF | Maximum 16-bit value |
FAQs
Denary is another word for decimal—the base-10 number system we use every day. It’s called “denary” because it uses ten digits (0-9), with each position representing a power of ten.
Hexadecimal provides a compact way to represent binary data. Four binary digits (bits) equal one hex digit, so programmers can write shorter, more readable codes. It’s particularly useful for memory addresses, colour codes, and debugging.
Multiply each hex digit by 16 raised to its position power (starting from 0 on the right), then add the results. For example, 2F = (2 × 16¹) + (15 × 16⁰) = 32 + 15 = 47.
Computers represent negative numbers using two’s complement notation in binary, which can then be expressed in hexadecimal. However, the standard denary-to-hex conversion process applies only to non-negative whole numbers.
FF represents the largest two-digit hexadecimal number, which equals 255 in denary. This is why RGB colour values range from 00 to FF—they need to fit within one byte (8 bits) of computer memory.
No. The letters A-F in hexadecimal can be written in uppercase or lowercase. Both 2A and 2a represent the same value (42 in denary). However, most programming conventions prefer uppercase.
Yes. Most exam boards want to see your method. Write out each division step with quotients and remainders clearly shown. Even if you make a small error, you can still earn method marks.
The 0x prefix indicates that the following number is hexadecimal. So 0x1A means 1A in hex (26 in denary). Different programming languages use various notations, including &H, #, or simply appending ‘h’.
Yes, but it requires a different method involving multiplication rather than division. The converter on this page handles whole numbers only, which covers most practical computing applications.
Hexadecimal needs 16 distinct symbols. Since we only have ten digits (0-9), the letters A through F represent values 10 through 15. This is perfectly normal—they’re not variables but actual digits in the base-16 system.