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A combinational circuit accepts a 3-bit binary number as input and generates a 4-bit binary number as output

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A combinational circuit accepts a 3-bit binary number as input and generates a 4-bit binary number as output. The output is the binary product of the decimal multiplication (see the table below). In the multiplication concerned, the 3-bit input should be considered as a signed number expressed in 3-bit signed 2s complement form, and the product should be expressed in binary using 4-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 3-bit input is even (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 as outputs. (b) Use a 4-to—l—line QUAD multiplexer to implement the outputs 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. Use a block diagram with appropriate labels for inputs and outputs to represent the multiplexer (i.e., you do not need to draw the internal structures of the multiplexer).