What is the decimal equivalent of the base-4 number '132'?

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Question: What is the decimal equivalent of the base-4 number \'132\'?

Options:

Correct Answer: 26

Solution:

\'132\' in base-4 is 1*16 + 3*4 + 2 = 26.

What is the decimal equivalent of the base-4 number '132'?

What is the decimal equivalent of the base-4 number '132'?

Step 1: Identify the base-4 number, which is '132'.
Step 2: Understand that in base-4, each digit represents a power of 4, starting from the rightmost digit.
Step 3: Write down the powers of 4 for each digit in '132':
- The rightmost digit (2) is in the 4^0 place (which is 1).
- The middle digit (3) is in the 4^1 place (which is 4).
- The leftmost digit (1) is in the 4^2 place (which is 16).
Step 4: Multiply each digit by its corresponding power of 4:
- 1 (from '132') * 16 (4^2) = 16
- 3 (from '132') * 4 (4^1) = 12
- 2 (from '132') * 1 (4^0) = 2
Step 5: Add all the results together: 16 + 12 + 2 = 30.
Step 6: The decimal equivalent of the base-4 number '132' is 30.

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