Decimal equivalent of the hexadecimal number (ADD)$$_{16}$$​ is:

Correct option is D

To convert the hexadecimal number (ADD)$$_{16}$$​ to its decimal equivalent, we need to expand it using powers of 16. Each digit in the hexadecimal number represents a power of 16 based on its position from right to left, starting with position 0.
The hexadecimal number ADD is represented as:
​$$A \cdot 16^2 + D \cdot 16^1 + D \cdot 16^0$$​​
Now, let's break it down:
· A in hexadecimal is 10 in decimal.
· D in hexadecimal is 13 in decimal.
So:
​$$A \cdot 16^2 = 10 \cdot 256 = 2560$$​​
​$$D \cdot 16^1 = 13 \cdot 16 = 208$$​​
​$$D \cdot 16^0 = 13 \cdot 1 = 13$$​​
Now, adding these values together:
2560 + 208 + 13 = 2781
Thus, the decimal equivalent of the hexadecimal number (ADD)$$_{16}$$​ is 2781.
Important Key Points:
1. Hexadecimal (base-16) uses digits 0-9 and A-F, where A = 10, B = 11, C = 12, D = 13, E = 14 and F = 15.
2. Convert each digit to its decimal equivalent and multiply by the corresponding power of 16.
3. Sum the results to get the decimal equivalent.