Recipe for minimization as SOP, Three-Variable Map (2.1)

Recipe for minimization as SOP

• Enter 1s in the K-map for each product term in the function
• Group adjacent K-map cells containing 1s to obtain a product with fewer variables.
• Handle “boundary wrap” for K-maps of 3 or more variables.
• Realize that answer may not be unique

•Note variable ordering: (x,y,z), x is row, yz specify column.

•Each cell adjacent to four other cells (left/right edge wrap)

The types of structures that are either minterms or are generated by repeated application of the

minimization theorem on a three variable map are shown at right. Groups of 1, 2, 4, 8 are possible. An implicant of a function is a product term that can be used in a sum of products expression for that function, that is, the function is 1 whenever the implicant is 1 (and maybe other times, as well). From the point of view of the map, an implicant is a rectangle of 1, 2, 4, 8, . . . (any power of 2) 1’s. That rectangle may not include any 0’s.

Consider the function, F, of the following maps. The second map shows the first four groups of 2; the third map shows the other group of 2 and the group of 4.