Common Exponent Values

You'll see certain powers of $2$ again and again in programming. Memorize these:

$2^8 = 256$, $2^{10} = 1024$, $2^{16} = 65536$, $2^{20} \approx 10^6$, $2^{30} \approx 10^9$, $2^{32} \approx 4 \times 10^9$.

Why do these matter? $2^{31} - 1 = 2147483647$ is the max signed $32$-bit integer. $2^{63} - 1$ is the max signed $64$-bit integer. When a problem says $n \leq 10^9$, you know it fits in $32$ bits. When $n \leq 10^{18}$, you need $64$ bits.

Also useful: $10^3 \approx 2^{10}$. This shortcut converts between powers of $10$ and powers of $2$ quickly.