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To express 2010 in base 2, we use exactly 8 ones and 3 zeros. Find the next two integers in base 2 that use the same number of ones and zeros.

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First check to see if the claim about 2010 is correct by converting it to base 2. The straightforward and obvious thing to do next is to try counting forward from 2010, in base 2, and see if you find the numbers you seek. If that didn't work, or if you don't know how to do it, perhaps you should try explaining your difficulty and asking for more specific help. – MJD Dec 16 '12 at 2:17

2 Answers

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If you convert 2010 to base 2, you get 11111011010.

Can you see of a method to increase the number while maintaining the same number of ones and zeros?

Hint, leave the upper 5-msb's alone and play with the lower 6 to keep the number of 1's and 0's the same. You want the next higher numbers. Does that make sense?

Regards -A

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The next number is $2012_{10}=11111011100_2$. Because $2010_{10}=11111011010_2$.

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