The correct option is
A. 11, 12, 13 respectively.
Explanation of the Correct Answer
The hexadecimal number system, also known as base-16, uses sixteen distinct symbols to represent values. These symbols are:
- The digits 0 through 9 represent values zero to nine.
- The letters A through F (or a through f) represent values ten to fifteen.
Here’s how the letters correspond to their decimal values:
- A = 10
- B = 11
- C = 12
- D = 13
- E = 14
- F = 15
Now, looking specifically at the question, we need to find the decimal values for B, D, and E:
- B in hexadecimal is 11 in decimal.
- D in hexadecimal is 13 in decimal.
- E in hexadecimal is 14 in decimal.
Thus, the values of B, D, and E in decimal are
11, 13, and 14, respectively.
Why the Other Options are Incorrect
Now, let’s analyze the other options to understand why they are incorrect:
- Option B: 11, 13, 14 respectively
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This option incorrectly states the value of D. While B is correctly identified as 11, D should be 13, and E should be 14. However, the sequence is not correct as it does not match the values of B, D, and E in the order given.
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Option C: 13, 14, 15 respectively
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This option incorrectly assigns the values. It suggests that B is 13, D is 14, and E is 15. This is incorrect because B is 11, D is 13, and E is 14.
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Option D: 14, 16, 17 respectively
- This option is entirely incorrect. It suggests that B is 14, D is 16, and E is 17. In the hexadecimal system, there is no representation for 16 and 17 as single digits; they would be represented as 10 and 11 in hexadecimal.
Summary of Key Points
- The hexadecimal system uses digits 0-9 and letters A-F to represent values 0-15.
- B corresponds to 11, D corresponds to 13, and E corresponds to 14 in decimal.
- The correct answer is A. 11, 12, 13 respectively.
- Understanding the conversion between hexadecimal and decimal is crucial for working with different number systems.
Revision Summary
- Hexadecimal (base-16) uses digits 0-9 and letters A-F.
- B = 11, D = 13, E = 14 in decimal.
- The correct answer is A: 11, 12, 13 respectively.
- Familiarize yourself with hexadecimal values to avoid confusion in conversions.