Subset Sum - Problem Statement

Given an array of $n$ integers and a target sum $S$, determine if any subset of the array sums to exactly $S$. For example, with array $[3, 1, 4, 2]$ and target $5$, the answer is yes because $\{3, 2\}$ and $\{1, 4\}$ both sum to $5$. Constraints: $n \leq 20$. With $n$ this small, $2^n \approx 1$ million subsets is feasible to enumerate.

This is the simplest bitmask problem: iterate all subsets, check their sums. Before reading on, try to write the brute-force solution. How would you represent each subset? How would you compute its sum?