Which of the following is the correct representation of the decimal number 25 in

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Question: Which of the following is the correct representation of the decimal number 25 in base-8?

Options:

Correct Answer: 31

Solution:

25 in decimal is represented as \'31\' in base-8 (3*8^1 + 1*8^0 = 24 + 1 = 25).

Which of the following is the correct representation of the decimal number 25 in base-8?

Which of the following is the correct representation of the decimal number 25 in base-8?

Step 1: Understand that we need to convert the decimal number 25 into base-8.
Step 2: Find the largest power of 8 that fits into 25. The powers of 8 are 1 (8^0), 8 (8^1), and 64 (8^2). The largest power that fits is 8 (8^1).
Step 3: Determine how many times 8 fits into 25. 25 divided by 8 equals 3 with a remainder. So, we can use 3 as the coefficient for 8^1.
Step 4: Calculate how much 3 times 8 is. 3 times 8 equals 24.
Step 5: Subtract 24 from 25 to find the remainder. 25 minus 24 equals 1.
Step 6: The remainder of 1 corresponds to 8^0. So, we have 1 as the coefficient for 8^0.
Step 7: Combine the coefficients from steps 3 and 6. We have 3 for 8^1 and 1 for 8^0, which gives us '31' in base-8.

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