Expressing $2010_{2}$

Question

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.

Answer 1

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

Answer 2

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