CZ1101, Lab 2, Week 7, 25-30 August. Due Tuesday, 2 September, 1997

Submitting your answers by the due date.

1. Same as Lab 1, Prob. 2, write a MIPS assembly program to verify the formula for the sum of fourth power of natural numbers, i.e.,

   1^4 + 2^4 + 3^4 + 4^4 + ... + n^4 - 
   ((1 + n)n(1 + 2n)(-1 + 3n + 3n^2))/30 = 0,
   

   but for general value n. You may use any registers from $8 to $25, but code should be short and clearfully commented. Your program should work for any integer 0 <= n < N_max. Test for few values, e.g., n=0, 2, 5, 10, 100, 1000, -1, -7. You program will not work properly if n is sufficiently large. Why? Find the upper limit N_max if you can. What happens if n is negative? Submit your assembly program and report your findings and explanations with script.
2. About Characters and Strings: While many programs work primarily with numbers, others work with characters. Most computers today use 8-bit bytes represent characters, with the American Standard Code for Information Interchange (ASCII) being the representation that nearly everyone follows. Because of the popularity of strings in some programs, MIPS provides special instructions to move bytes. Load byte (lb) loads a byte from memory, placing it in the rightmost 8 bits of a register; the other 24 bits are set to 0. Store byte (sb) takes a byte from the rightmost 8 bits of a register and writes it to memory. Thus the sequence

   lb $3, 0($4)      # Read byte from source
   sb $3, 0($5)      # Write byte to destination
   

   copies a byte. Characters are normally combined into strings, which have a variable number of characters. C uses the convention that a string is terminated by a byte with the value 0.

   (3.31) [20] Write a program in MIPS assembly language that copy and count a string. The program takes a pointer to a null-terminated source string in register $4 and a pointer to the destination string in register $5. It copies the byte contents starting from memory location given in $4 to the destination starting from the address given in $5, until a null character (a byte of value zero) is reached. It stores a count of the total number of non-null characters in the string in register $2. Hint: Look at the program copy in Exercise 3.8 for ideas. You test your program with the following template to set up the string.

   # Template for the bcopy.s (string copy) program
    
         .data
   str:    .asciiz "a string--end\n"  # the source string
   str2:   .asciiz "test, more space?\n"     # destination string
   
         .text
   main:
   
      la $4, str                      # load in source string address
      la $5, str2                     # load destination address
   
   # Your code here
         ...
   
         ...
   # Your code end
      move $4, $2
      li $2, 1
      syscall                         # print out count
      li $2, 4
      la $4, str                      # print source string
      syscall
      li $2, 4
      la $4, str2                     # print destination string
      syscall
   
      j $31 
   

   If your code is correct, you should see a number (the length of the string) followed by two identical source strings when the program is run.

   Here are some translations of C terminology and our machine language: The words `pointer to a string' means: the starting address of the array of characters. String is nothing but an array of bytes representing characters. `Pointer to the third character' means: the address of the third character.