UGC NET CSE | November 2017 | Part 2 | Question: 33

Question

Which of the following regular expressions, each describing a language of binary numbers (MSB to LSB) that represents non-negative decimal values, does not include even values?

• A. $0^*1^+0^*1^*$
• B. $0^*1^*0^+1^*$
• C. $0^*1^*0^*1^+$
• D. $0^+1^*0^*1^*$

Where $\{+,\ * \}$ are quantification characters.

Answer 1

When a number is represented in binary form, for odd numbers, we have a 1 in the LSB while a 0 in LSB for even numbers.

So, only the language generated by option (3) $0^*1^*0^*1^+$ will, for sure, have a 1 in the LSB. So, this language won't contain any even numbers.

Answer: option (3)

Comments

Sorry, I said that before u edited

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no problem :)

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@ Rishabh Gupta 2

in question , it is also mentioned like non-negative ryt then, first digit should be 0 always then MSB should be like 0⁺ 

can you pls clarify my doubt ?

thanks in advance