4.3 Selection

To select the least number of groups (singles, pairs, quads, octs, etc.), we start with the largest size. In our example, we start with pairs. Since there are four pairs, we need to select the highest number of pairs that leaves the least number of singles.

Fortunately, we don’t have any singles. This means we only need to select enough pairs to cover all the 1s. In our case, we have multiple possible combinations of pairs: {a,b,d} and {b,c,d} will both cover all the 1s. It is okay to have multiple groups covering the same cell.

Selecting pairs {a,b,d} means the output function is W = XZ(a) + Y Z(b) + Y Z(d). Selecting pairs {b,c,d} means the output function is W = Y Z(b) + XY (c) + Y Z(d).