$($a$)$ Register modified: $t$0$

$($b$)$ Updated value: $t$0=$ $s$1<<2=0$x$1<<2=0$x$4$

$($c$)$ Next instruction: Line$2$

$($a$)$ Register modified: $t$0$

$($b$)$ Updated value: $t$0=$ $t$0+$ $s$0=0$x$4+0$x$4000=0$x$4004$

$($c$)$ Next instruction: Line$3$

$($a$)$ Register modified: $t$1$

$($b$)$ Updated value: $t$1=$ Value at memory address $0$x$4006($little$-$endian$)=0$x$4168($sign$-$extended to $0$xFFFF$4168)$

$($c$)$ Next instruction: Line$4$

$($a$)$ Register modified: $t$2$

$($b$)$ Updated value: $t$2=($$t$1<0)=(0$xFFFF$4168<0)=0$

$($c$)$ Next instruction: Line$5$

$($a$)$ No change in registers and memory

$($b$)$ Next instruction: Line$6$

$($a$)$ No change in registers and memory

$($b$)$ Next instruction: Line$7$

$($a$)$ Register modified: $t$1$

$($b$)$ Updated value: $t$1=$ $t$1-1=0$xFFFF$4167$

$($c$)$ Next instruction: Line$8$

$($a$)$ No change in registers and memory

$($b$)$ Next instruction: Line$10$

$($a$)$ Register modified: $t$1$

$($b$)$ Updated value: $t$1=$ $t$1+1=0$xFFFF$4168$

$($c$)$ Next instruction: None $($Direct jump to Line$10)$

$($a$)$ Memory modified: Address $0$x$4006=0$x$41$

$($b$)$ Next instruction: None $($End of program$)$

Explanation:

Line $1$: $s$1(0$x$1)$ is left$-$shifted by $2$ bits, resulting in $t$0=0$x$4.$

Line $2$: $t$0(0$x$4)$ is added to $s$0(0$x$4000),$ resulting in $t$0=0$x$4004.$

Line $3$: Loads the half$-$word from memory address $0$x$4004+2=0$x$4006($little$-$endian$)$ into $t$1.$ The value at $0$x$4006$ is $0$x$4168.$

Line $4$: Compares $t$1(0$xFFFF$4168)$ with $0.$ Since $t$1$ is not less than $0,$ $t$2$ is set to $0.$

Line $5$: Since $t$2$ is equal to $0,$ the branch is taken to Line$9.$

Line $6$: Not executed because the branch condition is not satisfied.

Line $7$: Not executed because the branch condition is not satisfied.

Line $8$: Unconditional jump to Line$10.$

Line $9$: Increases the value of $t$1$ by $1,$ making it $0$xFFFF$4168.$

Line $10$: Stores the byte value of $t$1(0$xFFFF$4168)$ at memory address $0$x$4004+2=0$x$4006,$ replacing $0$x$68$ with $0$x$68.$