## Understanding the Formula: Converting Hexadecimal to Decimal
**Introduction:**
In the digital world, numbers come in various formats, including hexadecimal and decimal. Understanding the conversion between these formats is crucial for programmers, designers, and anyone working with digital systems. This article will delve into the formula and steps involved in converting hexadecimal to decimal.
**Hexadecimal Number System:**
Hexadecimal is a base-16 number system that uses 16 digits (0-9 and A-F). It is commonly used in computer science and digital communication due to its compact representation of large numbers.
**Decimal Number System:**
Decimal is a base-10 number system that uses 10 digits (0-9). It is the most commonly used numerical system in everyday life and is the foundation of our arithmetic operations.
**Conversion Formula:**
The formula to convert a hexadecimal number (H) to its decimal equivalent (D) is:
“`
D = H1 * 16^(n-1) + H2 * 16^(n-2) + … + Hn * 16^0
“`
where:
* H1, H2, …, Hn are the hexadecimal digits of the number, starting from the highest power of 16
* n is the number of hexadecimal digits in the number
**Steps for Conversion:**
1. **Identify the hexadecimal digits:** Write down the hexadecimal number and identify each of its digits.
2. **Multiply each digit by its power of 16:** Multiply the first digit by 16^(n-1), the second digit by 16^(n-2), and so on.
3. **Add the products:** Sum the products obtained in step 2.
4. **Convert the result to decimal:** The sum obtained in step 3 is the decimal equivalent of the hexadecimal number.
**Example:**
Let’s convert the hexadecimal number B5 to decimal:
* B5 = B * 16 + 5 * 1
* B (11) * 16 = 176
* 5 * 1 = 5
* 176 + 5 = 181
Therefore, the decimal equivalent of B5 is 181.
**Conclusion:**
Converting hexadecimal numbers to decimal involves multiplying each digit by its respective power of 16 and then summing the products. Understanding this formula enables us to effortlessly convert hexadecimal numbers to their decimal counterparts, a key skill in the realm of digital systems.
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