(a) [5 marks] Find a function to detect an error in the representation of a decimal digit in Binary Code Decimal (BCD). In other words, write an equation with value 1 when the inputs are any one of the six unused bit combinations in the BCD code, and value 0 otherwise. (Hints: In BCD representation, every decimal digit is represented as follows: 00000,10001,20010,30011,40100,50101,60110,70111,81000, 9 - 1001). (b) [3 marks] Suppose that we have three binary variables X,Y, and Z for a full adder circuit. Y and Z are added by considering x as the previous carry. Variables S and C are used to store the resultant sum and the carry. Write down the truth table for the full adder circuit. (c) 22 marks] Draw the full adder circuit in (b) using a 3 -to-8 line decoder and two OR gates