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By Tom O'Meara

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18 (ii). Using the grids to model &-cell (ZXzy) 29 30 TOPICS IN E N G I N E E K I N G LOGIC 0 I 2 4 2 0 1 3 6 FIG. 19 (i). Directional grids for six variables INTRODUCTION: THE LOGICAL MATRIX 1*1 0 | 3 5 |3 J_Î_L 7 FIG. 19 (ii). Directional grids for six variables 31 32 TOPICS IN E N G I N E E R I N G LOGIC I n the expansion, factors in parentheses including the constant bj = I need not be written explicitly, analogously to the terms with aj = 0 in the first canonic form. Similarly, in the remaining terms, b^ = 0 may be understood (not written exn plicitly).

Laying down in succession y and X , we find the configura­ tion shown at (c). Now we m a y use either Y or Z to block off the two 0's i n TOPICS IN E N G I N E E R I N G LOGIC P\ X 1 3 5 f 7 X F I G . 16 (i). Set of six-variable contact grids I N T R O D U C T I O N : THE LOGICAL M A T R I X 2\ 3 1 6\ 7 à Ξ 3 6 7 ^ FIG. 16 (ii). Set of six-variable contact grids 26 TOPICS IN E N G I N E E R I N G LOGIC s\ z 5 6 7 \ 1 1 Z \ 1 4 5 6 7 \ FIG. 16 (iii). Set of six-variable contact grids INTRODUCTION: THE LOGICAL MATRIX 2 0 1 2 3 z 4 5 6 7 F I G .

24b, where the count ratios are now correct. We next check the second rule, construct­ ing the matrix of Fig. 24 c for this purpose. Here in the states corresponding to the I's in Fig. 24b we mark down the num­ ber of variables which have the value I. We find 10 states with a = 2 and 1 with a = 5. Since the second rule is satisfied by these counts for 5 variables, the function is symmetric, in the variables A, B, G, D, E. An ambiguous case discussed in the literature is one where the I/O ratios are satisfied, but the number of combinations for a given a is not correct.

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