Converting hexadecimal to decimal

Explanation:
To convert a hexadecimal number to decimal, we need to understand the positional value of each digit in the hexadecimal system.

In the hexadecimal system, each digit represents a value from 0 to 15. The digits 0-9 represent their respective values, while the letters A-F represent the decimal values 10-15.

Hexadecimal number: (3CD)16

Step 1: Identify the positional value of each digit in the hexadecimal number.

The hexadecimal number (3CD)16 has three digits: 3, C, and D.

The rightmost digit, D, is in the ones position.
The middle digit, C, is in the sixteens position.
The leftmost digit, 3, is in the sixteens cubed (or 256) position.

Step 2: Convert each digit to its decimal equivalent.

The decimal equivalent of the digit D is 13.
The decimal equivalent of the digit C is 12.
The decimal equivalent of the digit 3 is 3.

Step 3: Multiply each digit by its positional value.

The digit D (13) is in the ones position, so its positional value is 160 (16^0 = 1).
13 * 1 = 13

The digit C (12) is in the sixteens position, so its positional value is 161 (16^1 = 16).
12 * 16 = 192

The digit 3 (3) is in the sixteens cubed position, so its positional value is 162 (16^2 = 256).
3 * 256 = 768

Step 4: Add the results of the multiplication.

13 + 192 + 768 = 973

Answer:
Therefore, the hexadecimal number (3CD)16 is equivalent to the decimal number 973.