Question 4 (15%) A combinational circuit accepts a 3-bit binary number as input and generates a 5-bit binary number as output. The output is the binary product of the decimal multiplication (see the table below), where the product is expressed in binary using 5-bit signed 2s complement form. Don't care conditions can be used as the output if the calculation gives an overflow. 3-bit input is odd input × 3 3-bit input is even input × (-3) (a) Design the combinational circuit above. Show the design steps in your answer (starting from the truth table of the circuit, and follow the steps described in lecture), and draw one circuit diagram using AND gates, OR gates and inverters as the implementation. Use binary variables A, B, C as inputs, and P, Q, R, S, T as outputs. (b) Use a 4-to-1-line QUAD multiplexer to implement the outputs, excluding the sign bit output, of the circuit in part (a) above. In your design, connect the leftmost two bits of the inputs to the selection lines of the multiplexer.