In a base-4 number system, what is the decimal equivalent of the number '132'?

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Question: In a base-4 number system, what is the decimal equivalent of the number \'132\'?

Options:

Correct Answer: 12

Solution:

\'132\' in base 4 is calculated as 1*4^2 + 3*4^1 + 2*4^0 = 16 + 12 + 2 = 30.

In a base-4 number system, what is the decimal equivalent of the number '132'?

In a base-4 number system, what is the decimal equivalent of the number '132'?

Step 1: Identify the base of the number system. Here, the base is 4.
Step 2: Write down the number '132' and identify each digit's position from right to left: 2 is in position 0, 3 is in position 1, and 1 is in position 2.
Step 3: Convert each digit to decimal by multiplying it by 4 raised to the power of its position: 1 * 4^2, 3 * 4^1, and 2 * 4^0.
Step 4: Calculate each term: 1 * 4^2 = 1 * 16 = 16, 3 * 4^1 = 3 * 4 = 12, and 2 * 4^0 = 2 * 1 = 2.
Step 5: Add all the results together: 16 + 12 + 2 = 30.
Step 6: The decimal equivalent of '132' in base 4 is 30.

Base Conversion – Understanding how to convert numbers from one base to another, specifically from base-4 to decimal.
Exponentiation – Applying the concept of exponents in the context of base systems to calculate the value of each digit.