Quads:

A quad is a group of four 1s that are horizontally or vertically adjacent. They can be end-to-end or in the form of a square. A quad leads to removal of two variables and their complements. A quad can be visualized as two adjacent pairs as illustrated in Figure (a). There are three possible pairs in K-maps: Horizontally adjacent 1s quad (encircled 1s in Figure (a)), Square adjacent 1s quad (encircled 1s in Figure (b)) and vertically adjacent 1s quad (encircled 1s in Figure (c)). Let us assume the SOP equation of Figure (b) and simplify this.

Here the two variables C, D and their complements are getting removed thereby further simplifying the SOP equation and therefore the logic circuits.

(a)                                                  (b)                                          (c)

Figure: (a) Horizontally Adjacent 1s Quad, (b) Square Adjacent 1s Quad, and (c) Vertically Adjacent 1s Quad in K-maps