Hexadecimal to Decimal Converter

Table of Contents

• How does hexadecimal to decimal conversion work?
• Hexadecimal to decimal conversion formula
• Conversion process
• Example #1
• Example #2
• Hexadecimal to decimal conversion table

How does hexadecimal to decimal conversion work?

Converting a hexadecimal number to decimal involves transforming a base-16 number to its base-10 equivalent. In the hexadecimal system, numbers are represented using digits 0 through 9 and letters A through F, where A equals 10, B equals 11, C equals 12, D equals 13, E equals 14, and F equals 15. This system is widely used in computing to simplify binary representation.

Hexadecimal to decimal conversion formula

To convert a hexadecimal number to decimal, use the following formula:

Where:

• i is the position of the digit, starting from the right (with i = 0 for the least significant digit).
• n is the total number of digits in the hexadecimal number.

Conversion process

The step-by-step process to convert a hexadecimal number to decimal is as follows:

1. Write the hexadecimal number and assign powers of 16 to each digit, starting from 0 from the right.
2. Substitute each hexadecimal digit with its decimal equivalent.
3. Multiply each digit's value by 16 raised to the corresponding power.
4. Add all products to get the final decimal value.

Example #1

Convert the hexadecimal number 1A3 to decimal:

1. 3 × 16⁰ = 3
2. A × 16¹ = 10 × 16 = 160
3. 1 × 16² = 1 × 256 = 256

Sum: 256 + 160 + 3 = 419

The decimal number is 419.

Example #2

Convert the hexadecimal number 7F to decimal:

1. F × 16⁰ = 15 × 1 = 15
2. 7 × 16¹ = 7 × 16 = 112

Sum: 112 + 15 = 127

The decimal number is 127.

Hexadecimal to decimal conversion table