Use hexadecimal notation to represent the following bit pattern:

1101110000111111

Letters in your answer should be capitalized.

Question

Use hexadecimal notation to represent the following bit pattern:

1101110000111111

Letters in your answer should be capitalized.

BlackTom AI · Accepted Answer

Group the binary number into 4-bit nybbles (starting from the right) and convert each nybble to its hexadecimal digit.

1. Relevant knowledge points and concepts
- Hexadecimal (base 16) represents 4 binary bits per hex digit because 16 = 2^4.
- To convert binary to hex, split the binary string into 4-bit groups (nybbles) starting from the rightmost bit, then map each group to its decimal value 0–15 and then to the corresponding hex digit (0–9, A–F).
- Endianness does not change the order when writing a binary-to-hex representation; maintain the original left-to-right order of the bit string.

2. Step-by-step reasoning
- Given bit pattern: 1101110000111111
- Split into 4-bit groups from the right: 1101 1100 0011 1111

3. Intermediate calculations for each group
- 1101 (binary) = 1·2^3 + 1·2^2 + 0·2^1 + 1·2^0 = 8 + 4 + 0 + 1 = 13 → hex digit D
- 1100 (binary) = 1·8 + 1·4 + 0·2 + 0·1 = 12 → hex digit C
- 0011 (binary) = 0·8 + 0·4 + 1·2 + 1·1 = 3 → hex digit 3
- 1111 (binary) = 8 + 4 + 2 + 1 = 15 → hex digit F

4. Why the correct answer is correct
- Concatenating the hex digits in the original order yields DC3F. Each nybble maps exactly to the computed hex digit, so DC3F is a faithful base-16 representation of the 16-bit binary string.

5. Why other answers would be incorrect
- Common mistakes include grouping from the left instead of the right (which can misalign groups if the length isn’t a multiple of 4), miscomputing binary-to-decimal values (e.g., thinking 1101 = 11 instead of 13), or using lowercase letters (the prompt requires capitalized letters). Endianness confusion might lead to reversed ordering; that would be incorrect for a straightforward numeric representation.

6. Conclusion and confirmation
- The hexadecimal representation of 1101110000111111 is DC3F, which matches the provided correct answer DC3F.

Use hexadecimal notation to represent the following bit pattern: 1101110000111111 Letters in your answer should be capitalized.Short answer

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