If a number in base-6 is represented as '54', what is its decimal equivalent?

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Question: If a number in base-6 is represented as \'54\', what is its decimal equivalent?

Options:

Correct Answer: 32

Solution:

\'54\' in base 6 is calculated as 5*6^1 + 4*6^0 = 30 + 4 = 34.

If a number in base-6 is represented as '54', what is its decimal equivalent?

If a number in base-6 is represented as '54', what is its decimal equivalent?

Step 1: Identify the base of the number. The number '54' is in base-6.
Step 2: Break down the number '54' into its digits. The first digit is '5' and the second digit is '4'.
Step 3: Determine the place values for each digit. The leftmost digit (5) is in the 6^1 place, and the rightmost digit (4) is in the 6^0 place.
Step 4: Calculate the value of the leftmost digit. Multiply 5 by 6 raised to the power of 1: 5 * 6^1 = 5 * 6 = 30.
Step 5: Calculate the value of the rightmost digit. Multiply 4 by 6 raised to the power of 0: 4 * 6^0 = 4 * 1 = 4.
Step 6: Add the results from Step 4 and Step 5 together: 30 + 4 = 34.
Step 7: The decimal equivalent of '54' in base-6 is 34.

Base Conversion – Understanding how to convert numbers from one base to another, specifically from base-6 to decimal.
Positional Notation – Recognizing the significance of each digit's position in a number system, where each position represents a power of the base.