CZ1101, Tutorial 3, Week 8, 1-6 September, 1997

You should try the problems before going to the tutorial classes. You need not hand in the solutions. We'll discuss only some of the problems in the class. This set of problems (1-7) come from the textbook page 156-158, Exercises 3.5 to 3.7, 3.18, 3.19, and from page 258, Exercises 4.3 to 4.8.

(3.5) [5] In some cases a simple instruction set like MIPS can synthesize instructions found in richer instruction sets such as the VAX. The following VAX instruction subtract 1 from register $5, placing the difference back in register $5, and then branches to L1 if $5 > 0:
```
sobgtr $5, L1    # $5 = $5 - 1; if ($5 > 0) goto L1
```
The operation is described in the comment of the instruction to help explain the operation. What is the shortest sequence of MIPS (machine) instructions, that performs the same operation?
(3.6) [5] Show the single MIPS instruction or minimal sequence of instructions for this C statement:
```
a = b + 100;
```
Assume a corresponds to register $11 and b corresponds to register $12.
(3.7) [10] Show the single MIPS instruction or minimal sequence of instructions for this C statement:
```
x[10] = x[11] + c;
```
Assume c corresponds to register $13 and the array x begins at memory location 4,000,000.
(3.18) [5] The instruction
```
beq $2, $3, L1
```
will compare the contents of $2 and $3 and branch to L1 if they are equal. Unfortunately, there is no single instruction that can be used to compare $2 with an immediate value, such as 14 or -200. Look at the format for branch instructions and explain why. Write a sequence of MIPS instructions that will branch to L1 if $2 is equal to 14. Hint: It only takes two instructions.
(3.19) [30] Consider the following fragment of C code:
```
for(i = 0; i <= 100; ++i) {
   a[i] = b[i] + c;
}
```
Assume that a and b are arrays of words at addresses 1500 and 2000, respectively. Register $15 is associated with variable i and $16 with c. Write the code for MIPS. How many instructions are executed during the running of this code? How many memory data references will be made during execution?
(4.3-4.5) [11] Convert decimal number 512, -1,023, and -4,000,000, into 32-bit two's complement binary numbers, respectively.

(4.6-4.8) [15] What decimal number does each of the following two's complement binary number represent?

1111 1111 1111 1111 1111 1110 0000 1100
1111 1111 1111 1111 1111 1111 1111 1111
0111 1111 1111 1111 1111 1111 1111 1111