MINIMIZATION OF BOOLEAN FUNCTIONS 



1427 



31 



Table V — Determination of the Minimum Sum for 



5" = E (0. 1. 2, 3, 7, 14, 15, 22, 23, 29, 31) 

 (a) Determination of Prime Implicants 



V 





 



1 



2 



1 1 1 1 1 >/ 



(b) First Step in Selection of Basis Rows 

 1 2 3 7 14 22 15 23 29 31 



A 

 B 



C 

 D 

 E 

 F 



* 

 * 



(c) Minimum Sum 

 r = 2 ((0, 1, 2, 3), (7, 15, 23, 31), (29, 31), (22, 23), (14, 15)] 



T — Xi'XtXi + X3X2X1 + X6X4X3X1 + X6X4'X3X2 + X6'X4X3X2 



other member of the pair has crosses. Crosses in Hned-out cohimns are 

 not considered. In Table VI (a), rows A and B and rows B and C are 

 such pairs of rows since row B has crosses in columns 2, 3, and 6 and row 

 A has a cross in column 6 and row C has crosses in columns 2 and 3. A 

 convenient way to describe this situation is to say that row B covers 

 rows A and C, and to write B3A,BZ)C.If row i is selected as a sup- 

 plementary basis row and row i is covered by row j , which has the same 

 total number of crosses as row i, then it is possible to choose row j as a 

 basis row instead of row i since row j has a cross in each column in which 

 row i has a cross. 



The next step is to hne out any rows which are covered by other rows 

 in the same partition of the table, rows A and C in Table VI (a). If any 



