任何人都可以解决这个问题：简化布尔表达式 Z=A+A'B + A'B'C+ A'B'C'D

Question

任何人都可以解决这个问题:简化布尔表达式Z= a + a 'b + a 'b 'c + a 'b 'c 'd这个问题的最终答案是什么?

Answer 1

Z = A + A'B + A'B'C + A'B'C'D <br>
Z = A + A'(B + B'C + B'C'D)        (distributivity) 
Z = A + A'(B + B'(C + C'D))       (distributivity) 
Z = A + A'(B + B'(C(D+1) + C'D))  (null law) 
Z = A + A'(B + B'(CD + C + C'D))  (distributivity) 
Z = A + A'(B + B'(C + D(C + C'))) (distributivity) 
Z = A + A'(B + B'(C + D))         (inverse law) 
Z = A + A'(B + C + D)             (same 4 steps applied above) 
Z = A + B + C + D                 (same as above) 

因此，整个表达式实际上可以用这个规则求解:
A + A'B = A + B(吸收定律)