1434 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



Table IX — Table of Prime Implicants for Transmission 



^ = Z (0> 1. 2, 4, 5, 6, 7, 8, 9, 11, 13, 14, 15, 16, 18, 19, 20, 

 21, 23, 24, 25, 26, 27, 28, 29, 30) 

 The selection of row A is shown 

 1 2 4 8 16 5 6 9 18 20 24 7 11 13 14 19 21 25 26 28 15 23 27 29 30 



X 

 X 



X 

 X 



X 

 X 



X 

 X 



X 

 X 



X — X 



I 



X 

 X 



i 



2' 



ber of basis rows is [-^] + 1 = 7. Since the number of selected rows is 

 9 there is no guarantee that they correspond to a minimum sum. 



If such an approximation to a minimum sum is not acceptable, then 

 further work is necessary in order to reduce the number of selected rows. 

 For each of the selected rows, a check is made of whether any of the rows 

 in the lower part of the table (non-selected rows) have crosses in all 

 columns in which the selected row has circled crosses. In Table X row 

 E has a circled cross only in column 19; since row Y also has a cross in 

 coluimi 19 rows E and Y are labeled "a". Other pairs of rows which have 

 the same relation are labeled with lower case letters, b, c, d, e in Table X. 

 It is possible to interchange pairs of rows which are labeled Avith the same 

 lower case letter without violating the requirement that each column 

 must contain a cross from at least one selected row. If a non-selected row 

 is labeled with two lower case letters then it may be possible to replace 

 two selected rows by this one non-selected row and thereby reduce the 



