1422 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



Minimum Sum: 



T = Xi'xzXi + xiXipcz 



« 



Quine's method, as illustrated in Examples 3.1 and 3.2, becomes 

 unwieldly for transmissions involving either many variables or many 

 p-terms. This difficulty is overcome by simplifying the notation and 

 making the procedure more systematic. The notation is simplified by 

 discarding the expressions invoh'ing literals and using only the binarj^ 

 characters. This is permissible because the expressions in terms of literals 

 can always be regained from the binary characters. The theorem being 

 used to combine terms can be stated in terms of the binary characters 

 as follows: If two binary characters are identical in all positions except 

 one, and if neither character has a dash in the position in w^hich they 

 differ, then the two characters can be replaced by a single character 

 which has a dash in the position in which the original characters differ 

 and which is identical with the original characters in all other positions. 



Table II — Determination of Prime Implicants for Transmission 

 T = X) (0> 2, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 18, 19, 29, 30) 

 (a) I (b) II (c) III 



XiXiXzX-iXi X^XiXzX-iXi X^XiXzXiXi 



02 OOO-OV 0246 00--0V 



04 00-00\/ 028 10 O-O-OV 



08 0-OOOV 02 16 18 -00-0 



16 -OOOOa/ 048 12 0--00V 



4 12 - 1 V 



8 10 1 - v 



8 12 1 - V 



7 OOlllV 16 18 100-OV 



11 1 1 1 V 



13 01101a/ 67 0011- 



14 01110a/ 6 14 0-llOv/ 

 19 10 11a/ 10 U O 1 O 1 - 

 10 14 1 - 1 O V 



29 1 1 1 1 V 12 13 110- 



30 11110a/ 12 14 1 1 - V 



26 00-lOV 26 10 14 O-'lOV 



2 10 0-010a/ 46 12 14 0-1-OV 



2 18 -0010a/ 8 10 12 14 01--0\/ 



4 6 1 - V 



(d) IV 



XfiXiXzXiXl. 



02468 10 12 14 



