Quad

The karnaugh map uses Pairs, Quads and Octets to get simplified logic circuits.

QUAD

A quad is a group of 1's that are end to end (or) in the form of a square as shown in Fig. 2.20A & 2.20B, respectively∴

A quad means that two variables and their complements are the dropouts in the boolean equation.

In Fig.2.20A, the four 1's can be visualized as two horizontal pairs [2.20C].

In the first horizontal pair, one variable goes from complemented form to uncomplemented form i.e.,  to D. In second horizontal pair one variable goes from uncomplemented form to complemented form i.e., D to . So drop D and  in first and second horizontal pair.

So, for 1st horizontal pair, the equation is AB

for 2nd horizontal pair, the equation is ABC

The boolean equation for these two pairs is

Y = AB + ABC

Y = AB [C+]

The final form is

Y = AB

Thus, we can see two variables C and D and their complements drop out.

Note: In Fig. 2.20B, when we move horizontally, D is the variable that changes form. Similarly, when we move vertically B changes form. Therefore, here also we can drop two variables i.e., B,  and D, 

The simplified Boolean equation is

Y = AC