CS 354 - Exam 1


CS 354, version A ANSWER KEY Fall 2003		Name:___________________ ID:___________________ Login:_____________________
	Exam 2

No electronic devices may be used while taking this exam. Examples of devices not allowed are calculators, pagers, cell phones, wrist calculators/computers, laptop computers, pocket computers. Each student is allowed one 8.5 by 11 inch sheet of paper with handwritten notes. The notes may be on both sides of the paper.

Show all work, and do any/all calculations on the exam. Extra scratch paper may not be used.

Exam Score
Q 1 = _____ / 6
Q 2 = _____ / 8
Q 3 = _____ / 12
Q 4 = _____ / 10
Q 5 = _____ / 10
Total = _____ / 46

Question 1 (6 points)
(A) Identify a program error that the simulator catches at execution time.
While a program is executing, the simulator may catch

bad addresses

undefined opcodes (e.g., due to jumping into data)

arithmetic difficulties such as overflow or divide by zero

(B) Identify a program error that the simulator catches at assembly time.
While a program is being assembled, the simulator may catch

syntax errors such as the wrong number of operands, an undefined instruction mnemonic
labels that are used but not defined, and it may also catch labels that are defined multiple times

(C) Why would we choose to use a stack instead of a queue in a program?
We choose to use a stack instead of a queue because of the ordering in which data is generated and used. A stack gives us last-in-first-out, where a queue gives us first-in-first-out.

Question 2 (8 points)

Give a TAL synthesis for each of the MAL instructions. Assume that variable X has been assigned address 0xabcdef00 and contains the value 0xfedcba00.


    sw  $8, X                     rem  $8, $9, $10

    lui $1, 0xabcd                div  $9, $10
    ori $1, $1, 0xef00            mfhi $8
    sw  $8, 0($1)


    li  $12, -1                   add  $12, $15, 3

    addi $12, $0, -1              addi $12, $15, 3

Question 3 (12 points total) Consider this MAL program fragment:


       .
       .
       .
       move $a0, $t3
       jal  X
       li   $t1, -20
       beq  $t0, $t1, print_error_msg
       .
       .
       .


X:     sub  $sp, $sp, 28
       sw   $ra, 28($sp)

       sw   $s0, 20($sp)
       sw   $s1, 24($sp)


       sw   $a0, 32($sp)

       li   $s0, -50

       li   $a0, -1
       jal  Y

       lw   $a0, 32($sp)
       addi $s1, $s0, 100
       sw   $s1, ($a0)


       lw   $s0, 20($sp)
       lw   $s1, 24($sp)

       lw   $ra, 28($sp)
       add  $sp, $sp, 28
       jr   $ra

(A) (6 points) List all cases where this program fragment does NOT follow the MIPS procedure call, register usage, and parameter passing conventions.
There are 2 cases where this code fragement does not follow the conventions.

The register $t0 is live across the call to X. Therefore, it must be saved/restored.

$s registers are used in X, but are not properly saved/restored.

(B) (6 points) In the space to the right of the code, show modifications of the code for only procedure X such that procedure X does follow the conventions.

Question 4 (10 points total)
(A) (6 points) Give machine code (in binary, and in hexadecimal) for the TAL assembly language instruction


    bltz  $10, loop

Assume that the branch instruction is to be placed at address 0x88110024, and the label loop is assigned address 0x88110000.


The machine code format for bltz:
0000 01ss sss0 0000 iiii iiii iiii iiii

$s is $10, 01010

The immediate field is computed from 

 byte offset = target addr - ( 4 + bltz addr )
               0x 0x88110000 - ( 4 + 0x88110024 )

 order this operation to get a positive result, then find the
 additive inverse in 2's complement representation.
     0x88110028
  -  0x88110000
  -------------
     0x00000028, which in binary is 0000 0000 0010 1000

     take the 2's complement:
     0000 0000 0010 1000

     1111 1111 1101 0111  + 1  =  1111 1111 1101 1000

     Eliminate the least significant 2 zeros (because we needed
     a word offset, not a byte offset), AND sign extend to form
     a 16-bit value.

0000 0101 0100 0000 iiii iiii iiii iiii
becomes
0000 0101 0100 0000 1111 1111 1111 0110
0x 0    5    4    0    f    f    f    6

(B) (4 points) What addressing modes are used for (each of) the operands in the machine code version of the branch instruction?
The first operand is register mode, and the second is a PC-relative addressing mode in the machine code.

Question 5 (10 points)
(A) (4 points) A 2-dimensional array of integers is stored in row major order. Assume that row and column indices start at 0. Assume the following MAL declarations, and write an equation for the address of element [Y, X].


   .data
array:        .word   0:200
num_rows:     .word   20
num_cols:     .word   10

addr of [Y,X] =  base address + size of an element *
                        
                       ( num_cols * Y  +  X ) 

              =  base address + 4 ( 10 * Y  +  X )

(B) (6 points) Write a MAL code fragment that places the integer value 33 into this array at location [Y, X], where the value for Y is in $8, and the value for X is in $9. Assume values for these variables have been set at some earlier point within the program. The code fragment will NOT check for indices out of range. Use comments to identify the contents of registers within the code fragment. Choose registers without regard of the MIPS conventions for register usage.

#  addr of [Y,X] =  base address + size of an element *
#                       ( num_cols * Y  +  X ) 

  la   $10, array            #  $10 is the base address
  lw   $11, num_cols         #  $11 is num_cols
  mul  $12, $11, $8          #  $12 will be the address of the word change
  add  $12, $12, $9
  mul  $12, $12, 4           # multiply by the size of an element in bytes
  add  $12, $12, $10         # add in the base address of array
  li   $13, 33               # $13 is the value to be placed at [Y,X]
  sw   $13, 0($12)