Question 2: (10 + 30+5 + 10 + 5) = 60 points) Design a 4-bit combinational circuit 2's complementer. The circuit generates at the output the 2's complement of the input binary numbers represented with 4 bits. Answer the following questions: (1) Complete the following truth table. A,B,C,D indicate the input binary number to be complemented using 2's complement and W.X,Y, Z represent the output 2's complement of the input binary number. The variable D is the least significant bit and A is the most significant bit of the binary number. (i) Simplify the Boolean function W in its Sum of Products form using K-Map | Show all your calculations/steps to obtain full marks. (iii) Show that the Boolean function W can be constructed using exclusive-OR gates Show all your calculations/steps to obtain full marks. (iv) Implement the function Z in its Product of Sums form with a decoder constructed with NAND gates (see figure below) and external gate (s) connected to the decoder outputs. (iv) Implement the function Z in its Product of Sums form with a decoder constructed with NAND gates (see figure below) and external gate (s) connected to the decoder outputs. + A B D OOOOOO Do D1 D2 D3 D4 Ds D6 4-to-16 D7 Ds DECODER DE D10 D11 D12 D13 D14 D15 + (v) Implement the function X with a Multiplexor