Electrical Engineering ⇒ Topic : Pairs, Quads, and Octets

Pairs, Quads, and Octets

If pairs, quads, and octets occur in K-map, encircle these at first. To obtain the SOP, let us discuss  these one by one with examples:

Pairs

       Figure (1) (a) shows an octet in K-map.

                                                           Figure (1) Horizontally next to each other..

Figure (1) (a) shows K-map for four variables. For the first '1', the product is ABCD and the second '1' represents the product ABCD . The output Y is given by

To achieve the above result by pairs, encircle two adjacent l's as shown in Figure 1(b).Since the pair is horizontal, therefore, AB is common The first 1 due to CD and the second 1 due to CD. Since D is common and e + c = 1, therefore, output is:

Figure (2) represents vertically adjacent pair.

                                     Figure (2) Vertically next to each other.

From Figure 2 (a), first '1' stands for ABCD and the second '1' stands for ABCD. The output Y is given by

Encircle the pair in Figure 2 (a), CD is common and AB and AB will be taken into account.

In AB and AB, B is common and X + A = 1.

Quads

Figure (3) shows two examples of quads.

                                         Figure (3) Example of quad.

In Figure 3 (a), the quad is horizontal and two pairs make a quad. For the first pair, output is AB e and for the second pair, output is ABC. For the horizontal quad, the resultant output is:

From Figure 3 (a), it is clear that for a horizontal quad, the output is the product of two variables corresponding to the row of horizontal quad

From Figure 3 (b), picking the first 1 and moving horizontally, the variable D changes form. The output for this pair (horizontal) is ABC. Picking the next 1 of the next row and moving horizontally, the output is ABC. The output for this quad is given by

Similarly, for vertical movement, the output for the first vertical pair is BCD and the output for the second vertical pair is BCD . Therefore, the output for this quad is given by

Octets

Figure 4 (a) shows an octet in K-map

                                                       figure (4) Example of Octet.

The octet in Figure 4 (a) is divided into two quads. For the first quad, the output is BC and for the second quad the output is BC. Therefore, the output for the octet is given by