Must the nop follow the jr?

Answer:

Yes. (Assuming a real MIPS chip with branch delays.) At run-time, there is no predicting what will be in memory after this jr.

This subroutine will be linked with other subroutines so we better be careful. It is likely that the linker will put another subroutine immediately after this one in memory, and that subroutine's prolog starts with:

sub     $sp,$sp,4      # push the return address
sw      $ra,($sp)

It would be disastrous to unintentionally execute that first instruction when our subroutine returns to its caller.

Maximum of Three Expressions

Say that some other programmer has been assigned this task:

Write a subroutine that returns the maximum of three expressions: x*x, x*y, and 5*y for integer arguments x and y. The integers use two's complement representation. Use stack-based linking.

With our stack-based linkage convention this is:

Subroutine maxExp
  Input:   $a0 -- x, a two's complement integer
           $a1 -- y, a two's complement integer
           
  Returns: $v0 -- the maximum of x*x, x*y, or 5*y

QUESTION 15:

Can this program use the subroutine maxInt?