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For any natural number , an ordering of all binary strings of length n is a Gray code if it starts with 0n, and any successive strings in the ordering differ in exactly one bit (the first and last string must also differ by one bit). Thus, for n = 3, the ordering (000, 100, 101, 111, 110, 010, 011, 001) is a Gray code. Which of the following must be TRUE for all Gray codes over strings of length n?
- a)the number of possible Gray codes is even
- b)the number of possible Gray codes is odd
- c)In any Gray code, if two strings are separated by k other strings in the ordering, then they must differ in exactly K + 1 bits
- d)In any Gray code, if two strings are separated by k other strings in the ordering, then they must differ in exactly k bits
- e)none of the above
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
For any natural number , an ordering of all binary strings of length n...
1). In the question it is stated that -> Thus, for n=3, the ordering (000, 100, 101, 111, 110, 010, 011, 001) is a Gray code.
2). We have to find orderings such that they start with 0n , must contain all bit strings of length n and successive strings must differ in one bit.
Option c&d are clearly wrong.
Now, consider n=1. The only Gray code possible is {0,1}. Hence no of Gray code = odd for n=1.
For n=2 only two Gray code exists {00, 10, 11, 01} and {00, 01, 11, 10}. Thus no of Gray code = even for n=2.
Thus it is not that gray codes could be only even or only odd.
Hence option e is correct.
2). We have to find orderings such that they start with 0n , must contain all bit strings of length n and successive strings must differ in one bit.
Option c&d are clearly wrong.
Now, consider n=1. The only Gray code possible is {0,1}. Hence no of Gray code = odd for n=1.
For n=2 only two Gray code exists {00, 10, 11, 01} and {00, 01, 11, 10}. Thus no of Gray code = even for n=2.
Thus it is not that gray codes could be only even or only odd.
Hence option e is correct.
Most Upvoted Answer
For any natural number , an ordering of all binary strings of length n...
Understanding Gray Codes
Gray codes are binary sequences where two successive values differ by only one bit. The sequence begins with the string of all zeros and must return to it after covering all possible strings of the same length.
Analyzing the Options
- Option A: The number of possible Gray codes is even
- This statement is not necessarily true. The number of distinct Gray codes is not predetermined to be even; it can vary based on the structure of the code.
- Option B: The number of possible Gray codes is odd
- Similar to option A, there is no inherent property of Gray codes that guarantees an odd quantity. The total number can be both odd or even depending on how they are constructed.
- Option C: If two strings are separated by k other strings, they must differ in exactly k + 1 bits
- This is incorrect. The distance between two strings in a Gray code doesn't have a fixed relationship with the number of strings separating them.
- Option D: If two strings are separated by k other strings, they must differ in exactly k bits
- This statement is also false. The condition that relates the separation and the bit difference does not hold in Gray codes.
Conclusion: Why Option E is Correct
- None of the Above
- Since options A, B, C, and D are all incorrect, the correct answer is option E: none of the above. Gray codes have specific properties, but none of the statements made in the options hold true universally for all Gray codes.
In summary, the nature of Gray codes does not support any of the statements provided in options A through D, confirming that option E is the valid choice.
Gray codes are binary sequences where two successive values differ by only one bit. The sequence begins with the string of all zeros and must return to it after covering all possible strings of the same length.
Analyzing the Options
- Option A: The number of possible Gray codes is even
- This statement is not necessarily true. The number of distinct Gray codes is not predetermined to be even; it can vary based on the structure of the code.
- Option B: The number of possible Gray codes is odd
- Similar to option A, there is no inherent property of Gray codes that guarantees an odd quantity. The total number can be both odd or even depending on how they are constructed.
- Option C: If two strings are separated by k other strings, they must differ in exactly k + 1 bits
- This is incorrect. The distance between two strings in a Gray code doesn't have a fixed relationship with the number of strings separating them.
- Option D: If two strings are separated by k other strings, they must differ in exactly k bits
- This statement is also false. The condition that relates the separation and the bit difference does not hold in Gray codes.
Conclusion: Why Option E is Correct
- None of the Above
- Since options A, B, C, and D are all incorrect, the correct answer is option E: none of the above. Gray codes have specific properties, but none of the statements made in the options hold true universally for all Gray codes.
In summary, the nature of Gray codes does not support any of the statements provided in options A through D, confirming that option E is the valid choice.
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For any natural number , an ordering of all binary strings of length n is a Gray code if it starts with 0n, and any successive strings in the ordering differ in exactly one bit (the first and last string must also differ by one bit). Thus, for n = 3, the ordering (000, 100, 101, 111, 110, 010, 011, 001) is a Gray code. Which of the following must be TRUE for all Gray codes over strings of length n?a)the number of possible Gray codes is evenb)the number of possible Gray codes is oddc)In any Gray code, if two strings are separated by k other strings in the ordering, then they must differ in exactly K + 1bitsd)In any Gray code, if two strings are separated by kother strings in the ordering, then they must differ in exactly k bitse)none of the aboveCorrect answer is option 'E'. Can you explain this answer?
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For any natural number , an ordering of all binary strings of length n is a Gray code if it starts with 0n, and any successive strings in the ordering differ in exactly one bit (the first and last string must also differ by one bit). Thus, for n = 3, the ordering (000, 100, 101, 111, 110, 010, 011, 001) is a Gray code. Which of the following must be TRUE for all Gray codes over strings of length n?a)the number of possible Gray codes is evenb)the number of possible Gray codes is oddc)In any Gray code, if two strings are separated by k other strings in the ordering, then they must differ in exactly K + 1bitsd)In any Gray code, if two strings are separated by kother strings in the ordering, then they must differ in exactly k bitse)none of the aboveCorrect answer is option 'E'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about For any natural number , an ordering of all binary strings of length n is a Gray code if it starts with 0n, and any successive strings in the ordering differ in exactly one bit (the first and last string must also differ by one bit). Thus, for n = 3, the ordering (000, 100, 101, 111, 110, 010, 011, 001) is a Gray code. Which of the following must be TRUE for all Gray codes over strings of length n?a)the number of possible Gray codes is evenb)the number of possible Gray codes is oddc)In any Gray code, if two strings are separated by k other strings in the ordering, then they must differ in exactly K + 1bitsd)In any Gray code, if two strings are separated by kother strings in the ordering, then they must differ in exactly k bitse)none of the aboveCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For any natural number , an ordering of all binary strings of length n is a Gray code if it starts with 0n, and any successive strings in the ordering differ in exactly one bit (the first and last string must also differ by one bit). Thus, for n = 3, the ordering (000, 100, 101, 111, 110, 010, 011, 001) is a Gray code. Which of the following must be TRUE for all Gray codes over strings of length n?a)the number of possible Gray codes is evenb)the number of possible Gray codes is oddc)In any Gray code, if two strings are separated by k other strings in the ordering, then they must differ in exactly K + 1bitsd)In any Gray code, if two strings are separated by kother strings in the ordering, then they must differ in exactly k bitse)none of the aboveCorrect answer is option 'E'. Can you explain this answer?.
For any natural number , an ordering of all binary strings of length n is a Gray code if it starts with 0n, and any successive strings in the ordering differ in exactly one bit (the first and last string must also differ by one bit). Thus, for n = 3, the ordering (000, 100, 101, 111, 110, 010, 011, 001) is a Gray code. Which of the following must be TRUE for all Gray codes over strings of length n?a)the number of possible Gray codes is evenb)the number of possible Gray codes is oddc)In any Gray code, if two strings are separated by k other strings in the ordering, then they must differ in exactly K + 1bitsd)In any Gray code, if two strings are separated by kother strings in the ordering, then they must differ in exactly k bitse)none of the aboveCorrect answer is option 'E'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about For any natural number , an ordering of all binary strings of length n is a Gray code if it starts with 0n, and any successive strings in the ordering differ in exactly one bit (the first and last string must also differ by one bit). Thus, for n = 3, the ordering (000, 100, 101, 111, 110, 010, 011, 001) is a Gray code. Which of the following must be TRUE for all Gray codes over strings of length n?a)the number of possible Gray codes is evenb)the number of possible Gray codes is oddc)In any Gray code, if two strings are separated by k other strings in the ordering, then they must differ in exactly K + 1bitsd)In any Gray code, if two strings are separated by kother strings in the ordering, then they must differ in exactly k bitse)none of the aboveCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For any natural number , an ordering of all binary strings of length n is a Gray code if it starts with 0n, and any successive strings in the ordering differ in exactly one bit (the first and last string must also differ by one bit). Thus, for n = 3, the ordering (000, 100, 101, 111, 110, 010, 011, 001) is a Gray code. Which of the following must be TRUE for all Gray codes over strings of length n?a)the number of possible Gray codes is evenb)the number of possible Gray codes is oddc)In any Gray code, if two strings are separated by k other strings in the ordering, then they must differ in exactly K + 1bitsd)In any Gray code, if two strings are separated by kother strings in the ordering, then they must differ in exactly k bitse)none of the aboveCorrect answer is option 'E'. Can you explain this answer?.
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For any natural number , an ordering of all binary strings of length n is a Gray code if it starts with 0n, and any successive strings in the ordering differ in exactly one bit (the first and last string must also differ by one bit). Thus, for n = 3, the ordering (000, 100, 101, 111, 110, 010, 011, 001) is a Gray code. Which of the following must be TRUE for all Gray codes over strings of length n?a)the number of possible Gray codes is evenb)the number of possible Gray codes is oddc)In any Gray code, if two strings are separated by k other strings in the ordering, then they must differ in exactly K + 1bitsd)In any Gray code, if two strings are separated by kother strings in the ordering, then they must differ in exactly k bitse)none of the aboveCorrect answer is option 'E'. Can you explain this answer?, a detailed solution for For any natural number , an ordering of all binary strings of length n is a Gray code if it starts with 0n, and any successive strings in the ordering differ in exactly one bit (the first and last string must also differ by one bit). Thus, for n = 3, the ordering (000, 100, 101, 111, 110, 010, 011, 001) is a Gray code. Which of the following must be TRUE for all Gray codes over strings of length n?a)the number of possible Gray codes is evenb)the number of possible Gray codes is oddc)In any Gray code, if two strings are separated by k other strings in the ordering, then they must differ in exactly K + 1bitsd)In any Gray code, if two strings are separated by kother strings in the ordering, then they must differ in exactly k bitse)none of the aboveCorrect answer is option 'E'. Can you explain this answer? has been provided alongside types of For any natural number , an ordering of all binary strings of length n is a Gray code if it starts with 0n, and any successive strings in the ordering differ in exactly one bit (the first and last string must also differ by one bit). Thus, for n = 3, the ordering (000, 100, 101, 111, 110, 010, 011, 001) is a Gray code. Which of the following must be TRUE for all Gray codes over strings of length n?a)the number of possible Gray codes is evenb)the number of possible Gray codes is oddc)In any Gray code, if two strings are separated by k other strings in the ordering, then they must differ in exactly K + 1bitsd)In any Gray code, if two strings are separated by kother strings in the ordering, then they must differ in exactly k bitse)none of the aboveCorrect answer is option 'E'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice For any natural number , an ordering of all binary strings of length n is a Gray code if it starts with 0n, and any successive strings in the ordering differ in exactly one bit (the first and last string must also differ by one bit). Thus, for n = 3, the ordering (000, 100, 101, 111, 110, 010, 011, 001) is a Gray code. Which of the following must be TRUE for all Gray codes over strings of length n?a)the number of possible Gray codes is evenb)the number of possible Gray codes is oddc)In any Gray code, if two strings are separated by k other strings in the ordering, then they must differ in exactly K + 1bitsd)In any Gray code, if two strings are separated by kother strings in the ordering, then they must differ in exactly k bitse)none of the aboveCorrect answer is option 'E'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
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