Homework 1. Problem 1. The following code fragment processes an array and produces two values in registers $v0 and $v1:

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1 Homework 1 Problem 1 The following code fragment processes an array and produces two values in registers $v0 and $v1: add $v0, $zero, $zero add $v1, $zero, $zero add $t6, $zero, $zero sll $a2, $a1, 2 add $t0, $zero, $zero add $t7, $zero, $zero outer: add $t4, $a0, $t0 lw $t4, 0($t4) add $t5, $zero, $zero add $t1, $zero, $zero inner: sll $t2, $t1, 2 add $t3, $a0, $t2 lw $t3, 0($t3) bne $t3, $t4, skip addi $t5, $t5, 1 skip: addi $t1, $t1, 1 bne $t1, $a1, inner slt $t2, $t5, $t7 bne $t2, $zero, elsepart add $v0, $t6, $zero add $v1, $t7, $zero add $t6, $t4, $zero add $t7, $t5, $zero j next elsepart: slt $t2, $t5, $v1 bne $t2, $zero, next add $v0, $t4, $zero add $v1, $t5, $zero next: addi $t0, $t0, 4 bne $t0, $a2, outer

Assume that: The array consists of 5000 indexed 0 through 4999 Its base address is stored in $a0 Its size in words, (5000) is stored in $a1 a. Describe in one sentence what this code does.

2 Assume that: The array consists of 5000 indexed 0 through 4999 Its base address is stored in $a0 Its size in words, (5000) is stored in $a1 a. Describe in one sentence what this code does. Specifically, what will be returned in $v0 and $v1? Hint: you should first focus on the control of the program (for and while loops, if-then-else statements, loops indices and expressions that control while and if statements). b. What is the total number of instructions that are executed in this piece of code? Briefly explain the number of instructions executed in each loop (e.g. There are 5 instructions that are executed once before loop outer, there are 7 instructions in loop inner that are executed 10 times, etc.). You need not calculate the exact number of instructions, as we are looking only for a ballpark figure. You can make a worst case assumption about the number of instructions executed in certain cases. c. Assume that the code fragment is run on a machine with a 500MHz clock that requires the following number of cycles for each instruction. In the worst case, how many seconds will it take to execute this code? d. Consider the following two lines in the inner loop: add $t3, $a0, $t2 lw $t3, 0($t3) We need register $a0 to hold the base of the array and register $t1 to hold the index of the array. Consider an architecture that is similar to MIPS except that the two lines of code above can be combined into one as follows: lw $t3, $a0+$t2 The addressing mode that allows two registers to be added together is called indexed addressing. This additional addressing mode is available in the PowerPC architecture. Assume that we can modify MIPS architecture to provide indexed addressing mode. This means that for each data transfer instruction that uses the base and index of an array, one arithmetic instruction can be eliminated. Unfortunately, to accommodate this new addressing mode, the cycle time is increased by 20%. In the worst case, how many seconds will it take to execute the code listed above using the modified MIPS architecture? How much faster or slower compared to the original MIPS code? Assume that the modified lw instruction still takes 5 cycles

3 Problem 2 Consider the sequence of Fibonacci numbers where F(n) = 0, if n = 0; 1, if n = 1; F(n-1) + F(n-2), if n > 1; a. Write a MIPS procedure to compute the n-th Fibonacci number based on the procedure below: int fib (int n) { if (n==0) return 0; else if (n==1) else return 1; return fib(n-1) + fib(n-2); Note that: The procedure generates a recursive process The procedure is straight-forward, but is also hopelessly inefficient. Use comments to clearly explain the functionality of the code segments, individual instructions, or specific registers. This will assist us with grading your homework. b. Write a MIPS procedure to compute the n-th Fibonacci number based on the procedure below: int fib_iter (int a, int b, int count) { if (count==0) else return b; return fib_iter(a+b, a, count-1); Note that: The first two parameters of the fib_iter procedure, a and b, keep track of the two previous two Fibonacci numbers computed. To compute F(n) you have to make the procedure call fib_iter(1, 0, n). Problem 3 Pseudo instructions are not part of the MIPS instruction set but often appear in MIPS programs. For each pseudo instruction in the following table, produce a minimal sequence of actual MIPS instructions to accomplish the same thing. You may need to use $at for some of the sequences. In the following table, big refers to a specific number that requires 32 bits to represent and small to a number that can fit in 16 bits.

4 Note: You should not use any registers other than the registers in the pseudo instruction and the special $at register. Problem 4 Convert the following decimal values to both binary and hexadecimal representations using 8 bit two s complement. If you cannot convert to twos complement please explain why Problem 5 Given the following MIPS assembly code (and assuming all registers start at 0): addi $1, $0, 10 add $2, $1, $1 repeat: addi $2, $2, -3 nand $3, $2, $2 addi $1, $1, -2 bne $0, $1, repeat a) Translate the MIPS code into C Code that performs the same operations. Please use the

5 variable names reg1, reg2, and reg3 for $1, $2, and $3. b) How many times is the line, nand $3, $2, $2 executed? c) What is the final value of $3?

ECE/CS 552: Introduction to Computer Architecture ASSIGNMENT #1 Due Date: At the beginning of lecture, September 22 nd, 2010

ECE/CS 552: Introduction to Computer Architecture ASSIGNMENT #1 Due Date: At the beginning of lecture, September 22 nd, 2010 This homework is to be done individually. Total 9 Questions, 100 points 1. (8