| Popis: |
For a given completely specified Boolean function having 2 variables and defined by a truth table indicating the values (0 or 1) for each of the binary combinations XY of the function ƒ(X, Y), each (ordered) combination XY can be considered as being the coordinates of a point in a plane. With rectangular axes and with an identical scale in both axes, the 4 corresponding points are located at the vertices (summits) of a square. Consider for example the function defined by Table 8.1: Table 8.1 X Y ƒ(X, Y) 0 0 1 0 1 1 1 0 1 1 1 0 The 4 combinations 00, 01, 11 and 10 are represented geometrically by the 4 points A, B, C and D respectively (Fig. 8.2a), the vertices of a square in the plane OXY. To specify a function ƒ(X, Y) is to associate with Open image in new window Fig. 8.2 certain of these vertices the value 1 and the value 0 with others, or, equivalently, to choose a certain subset of the set of vertices for which the function ƒ(X, Y) takes the value 1. This subset is simply the characteristic set ƒ(X, Y) and its characteristic function is ƒ(X, Y). For a completely specified function, rather than indicating the value 0 or 1 alongside each vertex (as would be the case for a truth table) it is more convenient to indicate the characteristic set ƒ(X, Y) only. For this purpose it suffices to mark in a ‘heavy’ point at each vertex which forms the characteristic set (Fig. 8.2b, c, d). |
