In a base-8 number system, what is the product of '7' and '5'?

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Question: In a base-8 number system, what is the product of \'7\' and \'5\'?

Options:

Correct Answer: 40

Solution:

7*5 = 35 in decimal, which is \'43\' in base-8.

In a base-8 number system, what is the product of '7' and '5'?

In a base-8 number system, what is the product of '7' and '5'?

Step 1: Understand that we are working in a base-8 number system, which means the digits can only be from 0 to 7.
Step 2: Multiply the numbers '7' and '5' as you would in the decimal system: 7 * 5 = 35.
Step 3: Convert the decimal result (35) into base-8. To do this, divide 35 by 8 and find the quotient and remainder.
Step 4: When you divide 35 by 8, the quotient is 4 and the remainder is 3. This means 35 in decimal is represented as '43' in base-8.
Step 5: Therefore, the product of '7' and '5' in base-8 is '43'.

Base-8 Number System – Understanding how to perform arithmetic operations in a non-decimal base, specifically base-8 (octal), and converting results back to the appropriate base.
Multiplication in Different Bases – The process of multiplying numbers and understanding how to interpret the results in the context of the base being used.
Base Conversion – Converting a product from decimal to base-8 to express the final answer correctly.