In a base-6 number system, what is the product of '5' and '2'?

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Question: In a base-6 number system, what is the product of \'5\' and \'2\'?

Options:

Correct Answer: 12

Solution:

In base-6, \'5\' * \'2\' = 10 in decimal, which is \'12\' in base-6.

In a base-6 number system, what is the product of '5' and '2'?

In a base-6 number system, what is the product of '5' and '2'?

Step 1: Understand that we are working in base-6, which means the digits can only be 0, 1, 2, 3, 4, or 5.
Step 2: Multiply the numbers '5' and '2' as you would in decimal: 5 * 2 = 10.
Step 3: Convert the decimal result (10) into base-6. To do this, divide 10 by 6.
Step 4: When you divide 10 by 6, you get 1 as the quotient and 4 as the remainder (10 = 6*1 + 4).
Step 5: The quotient (1) is the next digit, and the remainder (4) is the last digit in base-6.
Step 6: Therefore, 10 in decimal is represented as '14' in base-6.

Base Conversion – Understanding how to perform arithmetic operations in a non-decimal base and convert results back to that base.
Multiplication in Base Systems – Applying multiplication rules within a specific base system, particularly base-6 in this case.