Doubt regarding the editorial

#1

After observing the technique to get first bit, we can see that if we XOR L and R, the most significant bit of this XOR will tell us the maximum value we can achieve i.e. let XOR of L and R is 1xxx where x can be 0 or 1 then maximum XOR value we can get is 1111 because from L to R we have all possible combination of xxx and it is always possible to choose these bits in such a way from two numbers such that their XOR becomes all 1.

I want to ask how do we know that after 1xxx , xxx will have all possible combination between 2 numbers?

#2

It is based on logic that, if L xor R is 1xxx, then the number 1000 would be greater than L and less than equal to R and the number 111 would be also greater than L and less than R, their xor would be 1111, which means all x could be 1

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#3

Oh! So you mean that for L xor R= 1xxx
There will be two numbers 1000 and 111 falling between L and R and therefore these will give us 1111.

#4

yes, so if L xor R is 1xxx, max xor would be 1111

#5

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