(Solved): 13. (5 points) Given only the following logic components: - One 4-bit adder (this is not full adde ...

13. (5 points) Given only the following logic components: - One 4-bit adder (this is not full adder) - One invertor gate Design and draw a circuit to do: $S=\{\begin{array}{ll}A+3,& \text{ if }M=0\\ A+5,& \text{ if }M=1\end{array}$ Where $\mathrm{A}$ is a 4-bit binary number ( $\mathrm{A}3\mathrm{A}2\mathrm{A}1\mathrm{A}0$ ), $\mathrm{S}$ is a 4-bit binary number (S3 S2 S1 S0), and $M$ is a single bit. Show the details of your solution to get the full mark. 12. (10 points) Design a 4-bit arithmetic combinational circuit that performs the following operations: * Both $\mathrm{A}$ and $B$ are 4-bit binary unsigned numbers $\left({\mathrm{A}}_3{\mathrm{A}}_2{\mathrm{A}}_1{\mathrm{A}}_0\right)$ and $\left({\mathrm{B}}_3{\mathrm{B}}_2{\mathrm{B}}_1{\mathrm{B}}_0\right)$ * ${\mathrm{M}}_{\underline{1}},{\mathrm{M}}_{\underline{0}}$ are the control inputs to the arithmetic unit, based on the values of $M_1$ and ${\mathrm{M}}_{\underline{0}}$ the arithmetic unit performs a specific operation. * $\mathrm{S}$ is the 4-bit output of the arithmetic unit $\left({\mathrm{S}}_3{\mathrm{S}}_2{\mathrm{S}}_1{\mathrm{S}}_0\right)$. * ${\mathrm{B}}^{?8}$ is the result of performing integer multiplication of the 4-bit number $\mathrm{B}$ by 8 (i.e., multiplying B by 2 three times). * $\mathrm{A}/4$ is the result of performing integer division of the 4-bit number A by 4 (i.e., dividing A by 2 twice). * In this question you are required to design the combinational logic circuit inside the arithmetic unit using the minimum number of the following components: invertors, 4-bit Comparator, 4-bit adders, and 4:1 Multiplexers. You are not allowed to use any other logic components. * use 2's complement arithmetic within the design of your circuit once needed. * Clearly mark the pins of any component you use by identifying its inputs, outputs, and controls, and explain your solution (No credit without fully explaining the circuit). * Hint: multiplication by 2 and division by 2 can be performed by shifting left and shifting right, respectively.