3. [6 points] Here is a problem that we would like to make a circuit for. Suppose that a circuit takes as input an unsigned 3-bit binary number (where the bits are denoted A, B, and C with A being the left-most bit and C being the right-most bit). The 3-bit binary number represents temperature values hence this circuit takes as input temperature values in the range 0 degrees in base-10 (000 in base-2) and 7 degrees in base-10 (111 in base-2) (both inclusive). The output of the circuit (denoted as Z) is 1 if temperature is less than 4 degrees in base-10; 0 otherwise. For example, if input combination is 010 in base-2 (2 degrees in base-10) then output will be 1. Similarly another example, if input combination is 101 in base-2 (5 degrees in base-10) then output will be 0. You can think of the output (Z) as I heating system that turns on (i.e. Z = 1) when the system temperature is too low (below 4 degrees), and turns off (i.e. Z=0) when the system temperature is acceptable (4 degrees and higher). a. Convert the problem into a truth table using the table below. The input sequence MUST BE IN CORRECT ORDER. Input Output A | B | C Z b. Write the Boolean expression for Z in SOP form