MINIMIZATION OF BOOLEAN FUNCTIONS 



1421 



XxX-lxzxl + X\X2XzXi = .T1.T2 X3 



10 



8 



"10 1' 

 9 



X1X2X3 Xi + 0:1X2X3 X4 = XiXzXz 



[1100] fl 10 1I [110-1 

 L 12 J L 13 J L 12,13 J 



XiXiXz + ^1X2X3 = Xi Xz 



[10 0-1 [110-1 [1-0 



L 8,9 J L 12,13 J [8,9,12 



.12,13 



Prime Implicants; 



X\ Xz , 



1-0 - 

 _8,9,r2,13_ 



Xi XzXi 



"0- 

 3 



-111 



:,7 J 



Minimum Sum; 

 Example 3.2 



T = XiXz + XiXzXi 



T = 2:(5, 7, 12, 13) 



Canonical Expansion: 



T = x(xix{xi^ + xlx-iXzXi^ + X\XiXzxl + X\XiXz a;4 



0' 



[0 10 1I [0 1 1 1I [110 

 L 5 J L 7 J [ 12 



X-lxixixii, + XxXiXzXi = X\ Xi Xi 

 XiXiXzXi + XiXiXzXi = .T2.T3 Xi 



'110 01 [110 1I [110 -1 

 _ 12 J L 13 J L 12,13 J 



110 1 

 13 



Prime Implicants: 



Xi X2 Xi , 



x^xz Xi , Xia:2X3 



[0 1 - 1I [- 1 1I [110-1 

 L 5,7 J L 5,13 J L 12,13 J 



