In a hexadecimal system, what is the decimal equivalent of the hexadecimal numbe

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Question: In a hexadecimal system, what is the decimal equivalent of the hexadecimal number \'A3\'? (2023)

Options:

Correct Answer: 163

Exam Year: 2023

Solution:

In hexadecimal, \'A\' represents 10 and \'3\' represents 3. Therefore, A3 = (10 * 16^1) + (3 * 16^0) = 160 + 3 = 163.

In a hexadecimal system, what is the decimal equivalent of the hexadecimal number 'A3'? (2023)

In a hexadecimal system, what is the decimal equivalent of the hexadecimal number 'A3'? (2023)

Step 1: Understand that hexadecimal is a base-16 system, where the digits go from 0 to 9 and then A to F.
Step 2: Identify the digits in the hexadecimal number 'A3'. Here, 'A' is the first digit and '3' is the second digit.
Step 3: Convert the hexadecimal digit 'A' to decimal. 'A' represents 10 in decimal.
Step 4: The second digit '3' is already in decimal, so it remains 3.
Step 5: Determine the place values for each digit. The first digit 'A' is in the 16's place (16^1) and the second digit '3' is in the 1's place (16^0).
Step 6: Calculate the decimal value of 'A': 10 * 16^1 = 10 * 16 = 160.
Step 7: Calculate the decimal value of '3': 3 * 16^0 = 3 * 1 = 3.
Step 8: Add the two decimal values together: 160 + 3 = 163.

Hexadecimal to Decimal Conversion – Understanding how to convert numbers from the hexadecimal system (base 16) to the decimal system (base 10) by using positional values.