$2)(20$ points$)$

$2$a$)$ Given the C$-$like code, answer the questions below. Note: $256$x $16$ 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$).$

$\backslash (\backslash$mathbf$\{2$ a $.2\}\backslash ))(5$ pts$)$ List all local storage with its minimum number of bits that should be used.

$```$

Inputs: A$[256][16],$ go $(1-$bit$)$

Outputs: done $(1-$bit$),$ totalsum$(??)$

Local Storage: $??$

while$(1)\{$

while$(!$go$)$;

done $=0$; totalsum $=0$; max $=0$;

for$($k $=0$; k $<mtext></mtext><mn>2</mn><mn>5</mn><mn>6</mn>$; k$++\{$

totalsum $=$ totalsum $+$ A$[$k$]$;

if$($A$[$k$]>$ max$)$

max $=$ A$[$k$]$;

$\}$

done$=1$;

$\}$

$```$

$2$b$)(10$ pts$)$ Given the following state diagram of a circuit with $1$ input $($w$)$ and $3$ outputs $($s$,$ t $,$ and u$),$ 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

bits

Note: if the output encoding cannot be used, put $-1$ as your answer.