Hexadecimal to Decimal Converter

What is Hexadecimal to Decimal Conversion?

Hexadecimal to decimal conversion is the process of transforming a number from base 16 (hexadecimal) to base 10 (decimal). This conversion is fundamental in computer science and digital systems, where hexadecimal is often used for its compact representation of binary data.

Conversion Method

The conversion from hexadecimal to decimal involves multiplying each digit by a power of 16 and summing the results. Each position in a hexadecimal number represents a power of 16, increasing from right to left.

Hexadecimal Digits

Hex | Decimal    Hex | Decimal
----+---------   ----+---------
 0  |   0         8  |   8
 1  |   1         9  |   9
 2  |   2         A  |  10
 3  |   3         B  |  11
 4  |   4         C  |  12
 5  |   5         D  |  13
 6  |   6         E  |  14
 7  |   7         F  |  15

Conversion Steps

1. Identify the position of each hexadecimal digit (starting from 0 on the right).
2. Multiply each digit's decimal value by 16 raised to its position power.
3. Sum all the resulting values.

Example

Let's convert the hexadecimal number 1A3 to decimal:

1A316 = (1 × 16²) + (10 × 16¹) + (3 × 16⁰)
                 = (1 × 256) + (10 × 16) + (3 × 1)
                 = 256 + 160 + 3
                 = 41910

Advantages of Hex to Decimal Conversion

• Essential for interpreting hexadecimal data in human-readable decimal form.
• Useful in programming, especially when dealing with memory addresses or color codes.
• Facilitates calculations and comparisons in decimal, which is more intuitive for most people.

Understanding hexadecimal to decimal conversion is crucial for anyone working with computer systems, programming, or digital design. It bridges the gap between the compact hexadecimal representation used in many technical contexts and the decimal system we use in everyday mathematics.