1426 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



Table IV — Prime Implicant Table for the 



Transmission of Table II 

 2 4 8 16 6 10 12 18 7 11 13 14 19 29 30 



B 



C 

 D 

 E 

 F 

 G 

 H 



X X X X 



X X 



XXX 



X X 



X X 



X 

 X 



an asterisk next to each row which contains the sole entry of any cohmm 

 (rows A, B, C, D, E, G, H, in Table IV). A line is then drawn through all 

 rows marked with an asterisk and through all columns in which these 

 rows have entries. This is done because the requirement that these col- 

 umns have entries in at least one basis row is satisfied by selecting the 

 rows marked with an asterisk as basis rows. When this is done for 

 Table IV, all columns are lined out and therefore the rows marked with 

 asterisks are the basis rows for this table. Since no alternative choice of 

 basis rows is possible, there is only one minimum sum for the transmis- 

 sion described in this table. 



5 ROW covering 



In general, after the appropriate rows have been marked with asterisks 

 and the corresponding columns have been lined out, there may remain 

 some columns which are not lined out; for example, column 7 in 

 Table V(b). When this happens, additional rows must be selected and 

 the columns in which these rows have entries must be lined out until 

 all columns of the table are lined out. For Table V(b), the selection of 

 either row B or row F as a basis row will cause column 7 to be lined out. 

 However, row B is the correct choice since it has more crosses than row 

 F. This is an example of the situation which was described earlier in 

 connection with the partitioning of prime implicant tables. Row B is 

 marked with two asterisks to indicate that it is a basis row even though 

 it does not contain the sole entry of any column. 



The choice of basis rows to supplement the single asterisk rows be- 

 comes more complicated when several columns (such as columns 2, 3, 

 and 6 in Table VI (a)) remain to be lined out. The first step in choosing 

 these supplementary basis rows is to determine whether any pairs of 

 rows exist such that one row has crosses only in columns in which the 



