How can we convert hexadecimal to decimal?

To convert a hexadecimal number to decimal, you multiply each hexadecimal digit by 16 raised to the power of its position (starting from 0 on the right) and then sum the results.

Here's a breakdown of the process:

1. Identify the Hexadecimal Digits: Hexadecimal uses 16 digits: 0-9 and A-F, where A=10, B=11, C=12, D=13, E=14, and F=15.

2. Determine Positional Values: Starting from the rightmost digit, assign each digit a positional value that is a power of 16. The rightmost digit has a positional value of 16⁰ (which is 1), the next digit to the left has a positional value of 16¹ (which is 16), the next is 16² (which is 256), and so on.

3. Multiply and Sum: Multiply each hexadecimal digit by its corresponding positional value (power of 16). Add all the products together.

Example:

Let's convert the hexadecimal number 2A3 to decimal.

• Digit Breakdown:

  • 3 is in the position 16⁰ = 1
  • A (which is 10) is in the position 16¹ = 16
  • 2 is in the position 16² = 256

• Calculation:
  (2 256) + (10 16) + (3 * 1) = 512 + 160 + 3 = 675

Therefore, the hexadecimal number 2A3 is equal to the decimal number 675.

Table for Hexadecimal to Decimal Conversion:

Hexadecimal Digit	Decimal Equivalent
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

In summary, hexadecimal to decimal conversion involves multiplying each hex digit by its corresponding power of 16 and summing the results, considering A-F represent the decimal values 10-15 respectively.