Which of the following is the correct representation of the decimal number 15 in

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Question: Which of the following is the correct representation of the decimal number 15 in base-2?

Options:

Correct Answer: 1111

Solution:

The decimal number 15 is represented as \'1111\' in binary.

Which of the following is the correct representation of the decimal number 15 in base-2?

Which of the following is the correct representation of the decimal number 15 in base-2?

Step 1: Understand that base-2 is also known as binary, which uses only two digits: 0 and 1.
Step 2: Start with the decimal number 15 and find the largest power of 2 that fits into it. The powers of 2 are 1, 2, 4, 8, 16, etc.
Step 3: The largest power of 2 that is less than or equal to 15 is 8 (which is 2^3).
Step 4: Subtract 8 from 15. This gives you 7 (15 - 8 = 7).
Step 5: The next largest power of 2 that fits into 7 is 4 (which is 2^2).
Step 6: Subtract 4 from 7. This gives you 3 (7 - 4 = 3).
Step 7: The next largest power of 2 that fits into 3 is 2 (which is 2^1).
Step 8: Subtract 2 from 3. This gives you 1 (3 - 2 = 1).
Step 9: The last power of 2 that fits into 1 is 1 (which is 2^0).
Step 10: Now, we have used 8, 4, 2, and 1. This means we have 1 in the 2^3, 2^2, 2^1, and 2^0 places.
Step 11: Write down the binary representation by placing a '1' in each of the used powers of 2 and '0' in the others. This gives us '1111'.

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