$(20$ points$)$

$2$a$)$ Given the C$-$like code, answer the questions below. Note: $25616$ Register File $($with $1$ read port and $1$ write port$)$ is used for $A$ in the code.

$2$a$\mathrm{.}1)(5$ pts$)$ Determine minimum number of bits for totalsum such that NO overflow occurs $($assume that all values in the register file A are positive number$).$ Explain how you get your answer $($no explanation, $0$ point$).$

$2$a$\mathrm{.}2)(5$ pts$)$ List all local storage with its minimum number of bits that should be used$\mathrm{.}2$b$)(10$ pts$)$ Given the following state diagram of a circuit with $1$ input $($w$)$ and $3$ outputs $($s$,$ t$,$ and $4),$ specify minimum numbers of D$-$FFs or minimum numbers of bits for the state register that should be used if$(3$ pts$)$ the binary encoding method is used $$ bits$(4$ pts$)$ the one$-$hot encoding method is used $$ bits$(3$ pts$)$ the output encoding method is used bitsNote: if the output encoding cannot be used, put $-1$ as your answer.