An Overview of Hexadecimal Numbers
The letters "Hexa" and "deci" in the phrase "hexadecimal" stand for the numbers "6" and "10," respectively. The 16-digit hexadecimal representation of numerals 0 through 9 and letters A through F is known as the hexadecimal number system. To put it another way, the first nine numbers or digits are represented as numbers, while the next six digits are represented by the letters A through F. The decimal number system, which has a base of 9, and hexadecimal are quite similar. Therefore, after 9 digits, the 10th digit is represented as a symbol - 10 as A, 11 as B, 12 as C, 13 as D, 14 as E and 15 as F.
What are Hexadecimal Numbers?
Since each digit has a weight of power 16, the hexadecimal number system is also known as a positional number system. Each subsequent digit is 16 times more important than the one before it. For example : \[7B{3_{16}}\] ,\[4B2{A_{16}},67{F_{16}}{\rm{ \;and }}{76_{16}}\]
Hexadecimal Addition of Numbers
The only difference between hex addition and decimal addition is the addition of the letters A, B, C, D, E and F. Here is an illustration of hex addition. Check the example provided below, and for further information, see the paragraph below it.
Example for Hexadecimal Addition
When numbers higher than 9 (the letters A through F) are present, hex addition includes calculating basic decimal addition while converting between hex and decimal. In the example, B + 8 equals 11 + 8 or 19.
Hexadecimal Table
You can perform hexadecimal addition much easier if you use the table below.
Hexadecimal Table
How to Add Hexadecimal Numbers
The decimal number system, which has a base of 9, and the hexadecimal are quite similar. We can very easily add hexadecimal numbers by understanding the hexadecimal table and following simple addition.
Let’s understand it with the help of a example:
Addition of Hexadecimal Numbers
Here, we will add from ones place:
So, 3 + 1 = 4
Now, add tens place with the help of the hexadecimal table
b + 2 = d
Add the hundredth place now.
f + 6 = 15 (1will be in carry)
7 + b = 12
And as 1 was in carry over, so 12 + 1 = 13
Now, at last 1 + 1 = 2
Thus, the final answer is 235d4.
Solved Examples
Example 1: Add the following hexadecimal number.
8AB + B78
Ans: 8AB + B78
We know:
8 + B = 13
A + 7 = 11
8 + B = 13
8AB + B78 = 1423
Thus, the answer is 1423.
Example 2: Add the following hexadecimal numbers.
D6E + 8C6
Ans: We know that
E + 6 = 14
6 + C = 12
D + 8 = 15
Thus,
D6E + 8C6
= 1634
Therefore, its sum will be 1634.
Example 3: What use does the hexadecimal number system serve?
Ans: Hexadecimal number system applications:
There is a way to write numbers in hexadecimal. Symbols are used when we write numbers. We continue adding digits and adding colour references until there are no more symbols left. Assembly language programming errors can also occur.
Conclusion
The hexadecimal number system is also referred to as a positional number system since each digit has a power 16 value. The importance of each digit after the first one increases by a factor of 16.
FAQs on Addition of Hexadecimal Numbers
1. What exactly is the hexadecimal number system?
The hexadecimal number system is a way of counting that uses a base of 16. Unlike the decimal system we use daily (which has a base of 10), it uses 16 unique symbols. These are the numbers 0 through 9 and the letters A, B, C, D, E, and F, where A represents 10, B represents 11, and so on, up to F representing 15.
2. What is the basic rule for adding two hexadecimal numbers?
To add hexadecimal numbers, you add them in columns from right to left, just like in regular maths. The key rule is: if the sum of a column is 16 or more, you subtract 16 from the sum, write down the result, and then carry over a 1 to the next column on the left.
3. Why is the hexadecimal system so important for computers?
The hexadecimal system is important because it provides a human-friendly way to represent binary code. Each hexadecimal digit can represent a group of exactly four binary digits. This makes it much easier and shorter for programmers to read and write computer instructions, memory addresses, or colour codes (like #FF5733) compared to long strings of 0s and 1s.
4. Can you show a simple example of adding hexadecimal numbers?
Certainly! Let's add 2B + 15 in hexadecimal.
1. Start with the rightmost column: B (which is 11) + 5 = 16.
2. Since the sum is 16, we subtract 16 to get 0. We write down 0.
3. We carry over a 1 to the next column.
4. Now add the next column: 1 (carry-over) + 2 + 1 = 4. We write down 4.
The final answer is 40.
5. How is adding in hexadecimal different from adding in the decimal system?
The main difference is the 'carry-over' point. In the decimal system (base-10), you carry over when a sum reaches 10. In the hexadecimal system (base-16), you only carry over when the sum reaches 16. Additionally, hexadecimal addition can involve letters (A-F) and the final answer can also contain letters.
6. Is it possible to get a letter as the result when adding two hexadecimal numbers?
Yes, it's very common. If the sum of a column is between 10 and 15, the result for that column is written as its corresponding letter. For example, if you add 8 + 6, the sum is 14. In hexadecimal, 14 is represented by the letter E.
7. Where can I see hexadecimal numbers being used in everyday technology?
You can find hexadecimal numbers in many places, including:
- Web Colours: In web design, colours are often defined by a 6-digit hex code, like #FFFFFF for white or #000000 for black.
- Error Messages: Computer systems often show error codes in hexadecimal to identify a specific problem.
- Network Addresses: The MAC address of your phone, computer, or router is a unique identifier written in hexadecimal.
