MINIMIZATION OF BOOLEAN FUNCTIONS 



1433 



Table VIII — Determination of the Minimum Sums for 



T = J2iO, 1, 2, 5, 6, 7, 9, 10, 11, 13, 14, 15) 



(a) (c) 



0:4X3X2X1 



15 



1 1 1 1 v 



A 

 B 

 C 

 D 

 E 

 F 



G 

 H 



(d) 



(e) 



(i) (0, 1) + (2, 6, 10, 14) + (5, 7, 13, 15) + ( 9, 11, 13, 15) 

 (ii) (0, 2) + (1, 5, 9, 13) + (6, 7, 14, 15) + (10, 11, 14, 15) 



Ti = X4'X3'X2' + X2X1' + X3X1 + X4X1 



Tii = X4'x3'xi' + X1X2' + X3X2 + X4X2 



of its crosses circled can be discarded without violating the requirement 

 that each column should have at least one cross from a selected row. 

 Rows with no circled entries are discarded (one by one, since removal of 

 one row may require more crosses to be circled) until each selected row 

 contains at least one circled cross. This completes the first step. The se- 

 lected rows now correspond to a first approximation to a minimum sum. 

 A check should be made to determine whether the number of selected 

 rows is equal to the minimum number of basis rows. In Table X there 

 are at most 4 crosses per row and 26 columns so that the minimum num- 



