Converting between Bases

In total, we saw that:

$2619_{10} $$\;= 2048 $$\:+\:512 $$\:+\:32 $$\:+\:16 $$\:+\:8 $$\:+\:2 $$\:+\:1 $$\;= 2^{11} $$\:+\:2^9 $$\:+\:2^5 $$\:+\:2^4 $$\:+\:2^3 $$\:+\:2^1 $$\:+\:2^0$

Now that we know what powers of $2$ 'go' into $2619_{10}$, we can write the string out.

If a power of $2$ was 'present' in the calculation (e.g., $11$), then we append the bit $1$ to the string. If, conversely, a power of $2$ was unused in the calculation (e.g., we didn't use $2^{10}$,) we add the bit $0$ to the string. We keep adding these bits from left to right.

As such, since the bits we've seen are $11, 9, 5, 4, 3, 1,$ and $0$, these are the only bits in our string that will be $1$: everything else will be $0$. Our resulting string of bits is:

$101000111011_2$

Conclusion: $2619_{10}$ is $101000111011_2$ in base 2.