Problem $1$: $(15$ points$)$ Determine the MSOP expression corresponding to the function table of Table $1.$ Simplify the expression using a Karnaugh map.

Table $1.$ Function Table

Problem $2$: $(\backslash (\backslash$mathbf$\{5\}\backslash )$ points$)$: Draw the circuit diagram of problem $1$ using NAND$-$bOR circuit implementation. Assume all inputs and outputs are active high. Clearly label the inputs and outputs of the circuit. Follow proper mixed logic design.