Converting from decimal (base-10) to hexadecimal (base-16) is a fundamental process in computing, often achieved using the division-remainder method. This method systematically breaks down the decimal number into its hexadecimal equivalent by repeatedly dividing by 16 and recording the remainders.
Understanding Decimal and Hexadecimal Systems
Before diving into conversion, it's essential to understand both number systems:
- Decimal (Base-10): This is the number system we use daily, employing ten unique digits (0-9). Each digit's position represents a power of 10 (e.g., 123 = 1 10^2 + 2 10^1 + 3 * 10^0).
- Hexadecimal (Base-16): This system uses sixteen unique symbols. It includes the digits 0-9 and then uses the letters A-F to represent the values 10-15. Hexadecimal is widely used in computing for its compact representation of binary data.
Here's a quick look at the hexadecimal digits and their decimal equivalents:
| Decimal Value | Hexadecimal Digit |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 8 |
| 9 | 9 |
| 10 | A |
| 11 | B |
| 12 | C |
| 13 | D |
| 14 | E |
| 15 | F |
Step-by-Step Decimal to Hexadecimal Conversion
The most common and straightforward method for converting a decimal number to hexadecimal involves repeated division by 16. Follow these steps:
- Divide by 16 and Note Remainder: Take the given decimal number and divide it by 16. Record the remainder of this division.
- Divide the Quotient: Take the quotient from the previous division and divide it by 16 again. Note the new remainder.
- Repeat Until Zero: Continue this process of dividing the quotient by 16 and recording the remainder until the quotient eventually becomes zero.
- Convert Remainders (10-15): If any of your recorded remainders are between 10 and 15, convert them to their corresponding hexadecimal letters (A for 10, B for 11, C for 12, D for 13, E for 14, and F for 15).
- Assemble the Hexadecimal Number: Read the remainders from the bottom up (the last remainder obtained is the most significant digit, and the first remainder is the least significant digit) to form the final hexadecimal number.
Example: Converting 255 to Hexadecimal
Let's convert the decimal number 255 to its hexadecimal equivalent.
- Step 1: $255 \div 16 = 15$ with a remainder of $15$.
- Step 2: $15 \div 16 = 0$ with a remainder of $15$.
Now, we have our remainders: $15$ and $15$.
Converting these remainders to hexadecimal digits:
- $15$ becomes F
- $15$ becomes F
Reading the remainders from bottom to top, we get FF.
Therefore, decimal 255 is FF in hexadecimal.
Example: Converting 4096 to Hexadecimal
Let's convert the decimal number 4096 to hexadecimal.
- Step 1: $4096 \div 16 = 256$ with a remainder of $0$.
- Step 2: $256 \div 16 = 16$ with a remainder of $0$.
- Step 3: $16 \div 16 = 1$ with a remainder of $0$.
- Step 4: $1 \div 16 = 0$ with a remainder of $1$.
Our remainders are: $0$, $0$, $0$, $1$.
All are already valid hexadecimal digits (0-9).
Reading the remainders from bottom to top, we get 1000.
Therefore, decimal 4096 is 1000 in hexadecimal.
Quick Reference Table: Decimal to Hexadecimal (0-32)
For smaller numbers, you can use a quick reference table:
| Decimal | Hexadecimal | 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 |
Practical Applications of Hexadecimal
Hexadecimal is extensively used in various technical fields due to its ability to represent large binary numbers concisely. Each hexadecimal digit corresponds to exactly four binary bits, making it a convenient shorthand.
- Computer Memory Addresses: Memory locations in computers are often represented in hexadecimal (e.g.,
0xFFFF). This makes addresses easier for humans to read and write than long binary strings. - Color Codes: In web design and digital graphics, colors are frequently specified using hexadecimal triplet values for Red, Green, and Blue (RGB). For example, pure red is
#FF0000, white is#FFFFFF, and black is#000000. You can explore HTML color codes for more examples. - MAC Addresses: Media Access Control (MAC) addresses, which uniquely identify network interfaces, are typically displayed in hexadecimal (e.g.,
00:1A:2B:3C:4D:5E). - Debugging and Low-Level Programming: Programmers and system administrators often encounter hexadecimal when working with assembly language, examining memory dumps, or analyzing network packets.
Tips for Accurate Conversion
- Double-Check Calculations: Always re-verify your division and remainder calculations, especially with larger numbers.
- Practice Regularly: The more you practice, the faster and more accurate you will become.
- Use Online Converters for Verification: While understanding the manual process is crucial, online decimal to hexadecimal converters can be useful for quickly checking your work.
Decimal to Hexadecimal Conversion
