How to Convert Hexadecimal to Decimal
Converting hexadecimal numbers to decimal is a fundamental operation in computer science and digital systems. Here's a comprehensive guide on how to perform this conversion:
The formula for converting a hexadecimal number to decimal is:
\[ \text{Decimal} = \sum_{i=0}^{n-1} (d_i \times 16^i) \]
Where:
\(d_i\) represents the decimal value of each hexadecimal digit
\(i\) is the position of the hexadecimal digit (starting from 0 for the rightmost digit)
\(n\) is the total number of hexadecimal digits
Conversion Steps
Identify each hexadecimal digit in the number.
Convert each hexadecimal digit to its decimal equivalent (0-9 remain the same, A=10, B=11, C=12, D=13, E=14, F=15).
Multiply each decimal equivalent by 16 raised to the power of its position (rightmost digit is position 0).
Sum all the resulting values.
Example Conversion
Let's convert the hexadecimal number 2A7 to decimal.
Step 1: Identify Hexadecimal Digits
The hexadecimal number 2A7 consists of three digits: 2, A, and 7.
Step 2: Convert Each Digit to Decimal
2 remains 2
A becomes 10
7 remains 7
Step 3: Multiply by Powers of 16
2 × 16² = 2 × 256 = 512
10 × 16¹ = 10 × 16 = 160
7 × 16⁰ = 7 × 1 = 7
Step 4: Sum the Results
512 + 160 + 7 = 679
Final Result
Therefore, 2A7 in hexadecimal = 679 in decimal
Visual Representation
2A7
Hexadecimal
Conversion Steps:
2 × 16² = 2 × 256 = 512
A(10) × 16¹ = 10 × 16 = 160
7 × 16⁰ = 7 × 1 = 7
512 + 160 + 7 = 679
Convert
679
Decimal
Position Values:
2 in position 2 (16²)
A(10) in position 1 (16¹)
7 in position 0 (16⁰)
Total = 679₁₀
This diagram illustrates the process of converting the hexadecimal number 0x2A7 to its decimal equivalent 679.