You are require to design a logic controller. A, B and C are three logic inputs and Y is the logic output of system. The requirement as following:
(1) If A and B are both 0,Y=1.
(2) If A is 1,Y=1.
(3) Others, Y=0
(a) Construct the truth table for Y.
(b) Develop the not simplified expression of Y in SOP form.
(c) Simplify Y by using K-map.
(d) Convert 1010(2) into a decimal number.