How to Convert Hexadecimal to Decimal?

Converting hexadecimal (base-16) numbers to decimal (base-10) involves understanding the positional value of each digit within the hexadecimal system. The process relies on multiplying each hexadecimal digit by powers of 16, corresponding to its position.

Understanding Hexadecimal Numbers

Hexadecimal is a base-16 number system, meaning it uses 16 unique symbols to represent values. Unlike the decimal system which uses 0-9, hexadecimal uses 0-9 and then A-F to represent the values 10-15.

Here's a quick reference for hexadecimal digits and their decimal equivalents:

Hexadecimal Digit	Decimal Value
0	0
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	8
9	9
A	10
B	11
C	12
D	13
E	14
F	15

For more details on number systems, you can refer to resources like W3Schools on Hexadecimal.

Step-by-Step Conversion Process

To convert a hexadecimal number to its decimal equivalent, you manually start multiplying each hex number by 16. Each digit's result is then determined by raising 16 to a power, starting from 0 for the rightmost digit and increasing by 1 for each subsequent digit to the left. Finally, sum up all these products.

Here are the detailed steps:

1. Identify Place Values: Assign a power of 16 to each digit of the hexadecimal number, starting from the rightmost digit with 16⁰. Increase the power by one for each digit moving to the left (16¹, 16², etc.).
2. Convert Hex Digits: Replace any alphabetic hexadecimal digits (A-F) with their decimal equivalents (10-15).
3. Multiply and Sum: Multiply each converted decimal digit by its corresponding power of 16.
4. Add the Products: Sum all the results from step 3 to get the final decimal number.

This method applies to any length of hexadecimal number. For a deeper dive into number system conversions, GeeksforGeeks provides comprehensive guides.

Example: Converting 2AF to Decimal

Let's convert the hexadecimal number 2AF to its decimal equivalent using the steps outlined above.

1. Assign Powers of 16:

   • The rightmost digit F corresponds to 16⁰.
   • The middle digit A corresponds to 16¹.
   • The leftmost digit 2 corresponds to 16².

2. Convert Hex Digits to Decimal:

   • F in hexadecimal is 15 in decimal.
   • A in hexadecimal is 10 in decimal.
   • 2 in hexadecimal is 2 in decimal.

3. Multiply Each Digit by its Power of 16:

   • For F: 15 * 16^0 = 15 * 1 = 15
   • For A: 10 * 16^1 = 10 * 16 = 160
   • For 2: 2 * 16^2 = 2 * 256 = 512

4. Sum the Products:
   15 + 160 + 512 = 687

Therefore, the hexadecimal number 2AF is equal to 687 in decimal.

Number System Conversion