1. In this exercise you have to complete a series of exercises to either prove or disprove that the following equivalence statement is true AB'C' + AB'C = AB a. Make a circuit for the Left Hand Side of the equivalence statement above using LogicGates.jar app. Take a snapshot of that circuit and paste below. b. Use the circuit you built in part a to complete the following table Output Left Hand Side ABC ABC laput ABC 000 001 010 011 100 101 110 c. Make a circuit for the Right Hand Side of the equivalence statement above using LogicGates.jar app. Take a snapshot of that circuit and paste below. d. Use the circuit you built in partc to complete the following table Output (Right Hand Side) Input ABC 000 001 010 O!! 100 101 111 e. Compare the truth tables from parts band d and state whether or not the equivalence statement holds. Give reasoning 2. Here is a problem that we would like to make a circuit for Suppose that a circuit takes as input an unsigned 4-bit binary number (where the bits are denoted A, B, C and D with A being the left-most bit and D being the right-most bit). The output of the circuit (denoted as Z) is 1 if the 4-bit binary number is between 0100 and 1011. (both inclusive), O otherwise a. Convert the problem into a truth table using the table below. The input sequence MUST BE IN CORRECT ORDER Input Output ABCD Z b. Write the Boolean expression for Zin SOP form. c. Simplify the expression from part b. Simplified expression may remain in SOP form. d. Draw the circuit for the simplified expression for Z using LogicGates.jar app. Take a snapshot of that circuit and paste below. Test your circuit in the app so that it matches the truth table for the problem above before you paste your circuit