The binary string 0011011 is a member of which of the following problems? Rememb

Question

The binary string 0011011 is a member of which of the following problems? Remember, a "problem" is a language whose strings represent the cases of a problem that have the answer "yes." In this question, you should assume that all languages are sets of binary strings interpreted as base-2 integers. The exception is the problem of finding palindromes, which are strings that are identical when reversed, like 0110110, regardless of their numerical value. a) Is the given string a composite number (not a prime)? b) Is the given string not a multiple of 3? c) Is the given string a palindrome? d) Is the given string greater than 50? The binary string 0011011 is a member of which of the following problems? Remember, a "problem" is a language whose strings represent the cases of a problem that have the answer "yes." In this question, you should assume that all languages are sets of binary strings interpreted as base-2 integers. The exception is the problem of finding palindromes, which are strings that are identical when reversed, like 0110110, regardless of their numerical value. a) Is the given string a composite number (not a prime)? b) Is the given string not a multiple of 3? c) Is the given string a palindrome? d) Is the given string greater than 50? The binary string 0011011 is a member of which of the following problems? Remember, a "problem" is a language whose strings represent the cases of a problem that have the answer "yes." In this question, you should assume that all languages are sets of binary strings interpreted as base-2 integers. The exception is the problem of finding palindromes, which are strings that are identical when reversed, like 0110110, regardless of their numerical value. a) Is the given string a composite number (not a prime)? b) Is the given string not a multiple of 3? c) Is the given string a palindrome? d) Is the given string greater than 50?

Explanation / Answer

Given string is (0011011)2 = (1+2+8+16)10 = 27

a). The given string represents the value 27. 27 is not a prime number. That means 27 is a composite number which implies that the given string is a composite number. Hence, option (a) is true.

b). 27 is a multiple of 3. Hence option (b) is false.

c). The reverse of the given string is (1101100) which is not the same as the given string. THerefore, it is not a palindrome and hence option (c ) is false.

d). 27 is not greater than 50. Therefore, the given string is not greater than 50 and hence, option (d) is false.

Therefore, option(a) is the correct answer.

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