CSC103 Homework 4 Fall 2012

--D. Thiebaut 13:26, 11 October 2012 (EDT)

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This homework is due on 10/18/12 at 9:00 a.m. You can work in pairs on this homework, but only if the work is done only when both people are together, and not when they are apart. If you work in pairs, simply put both names at the top of the document you will be handing in or submitting.

Misc. Information

If you haven't already read it, there is a lot of good information in the Introdcution to the xComputer and Introduction to Assembly Language documents.

Problem #1

You can hand-write the answers to this problem. Typed and printed answers are also acceptable, of course.

The program below computes the sum of all the numbers between 0 and 10. It is the final version of the program we developed in class on Thursday 10/11/12.

Note that I have added comments to the program. This helps make a very cryptic program easier to understand. In assembly language we can place comments in the code by preceding them with semicolons. The words following a semicolons are ignored by the translator when it takes the assembly-language program and puts the mnemonics in memory. If the comments bother you, you can simply put your cursor on each semicolon and remove the text on the right-hand side of it.

; Sum100 program
; D. Thiebaut
; Computes the sum of all the numbers between 0 and 10
; and stores the result in variable sum.
;

@0
        jmp start

;
; data section with 2 variables
;

counter: 10
sum:     0

;
; code section
;
start:

; sum <- counter
         lod    counter
         sto    sum

; counter <- counter - 1
loop:
     	 lod    counter
	 dec
	 sto    counter

; if counter is 0, then jump out of loop

         jmz    done

; sum <- sum + counter

         lod    sum
         add    counter
         sto    sum

; go back to compute new sum

         jmp    loop

; if we reach this point, then we are done with
; the loop and sum should contain the result

done:    hlt

Just to verify that the program works, copy/paste its code into the simulator (click here to get the applets). Run the program by selecting the fastest speed , and then clicking on Run.

Question 1

How many instructions are executed by the processor to compute the sum? In other words, from the time the processor executes the first jmp start instruction, to the time it executes hlt, how many instructions will it have executed, including the first and last? Be precise in your answer!

Question 2

How do you modify the program to make it compute the sum of 0 to 100?

Question 3

How many instructions are executed by the processor to compute the sum of 0 to 100?

Question 4

Assume that the processor operates at a 3 GHz frequency (given by the crystal). Assume furthermore that each instruction takes 1 cycle to execute. In this case a cycle is 1 / 3,000,000,000 second, or 0.33 ns. How long does it take the program to compute the sum of all the numbers between 0 and 10? Between 0 and 100? Between 0 and 1,000,000?

As a reminder,

• 0.001 sec = 1 ms (millisecond).
• 0.000001 sec = 1 µs (microsecond).
• 0.000000001 sec = 1 ns (nanosecond).

Submission

Hand in a copy of your answers on a sheet of paper, in class, on the due date.

Problem #2

You will need to submit your code electronically. More information below.

Using the program of Problem #1 as inspiration, write an assembly language program that computes the sum of all the even numbers between 0 and 100.

Check your program on the simulator.

Submission

• Go to this URL: http://cs.smith.edu/~thiebaut/103/submit4.htm
• You will see a simple submission form for your program.
• Enter the 2 letters that identify your wiki account. For example, if your wiki account was 103b-ac, then the two letters you need to enter in the box are ac.
• Enter 2 for the problem number
• Erase the line that reads

  ; Paste your program below this line (you may erase this line)

and replace it by your name, preceded by a semicolon. Example

  ; Mickey Mouse

If you worked with a partner on this program, write both names on separate lines, each with a semicolon as the first character:

  ; Mickey Mouse
  ; Donald Duck

• Paste your code below the line containing your name(s).
• Click on the submit button at the bottom of the page.

Problem #3

You need to submit your program electronically, as for Problem 2.

Write an assembly language program that computes 2 different sums, in 2 different variables, sum1 and sum2. When the program starts, both sum1 and sum2 contain 0. When the program ends, sum1 contains the sum of all the odd numbers between 0 and 100, and sum2 contains the sum of all the even numbers between 0 and 100. Write your program in such a way that you cannot assume that you already know that the sum of all the numbers between 0 and 100 is 5050. In other words, the number 5050 should not appear in your program as a constant or declared initially in a variable.

Recommentations

• Keep an eye for efficiency. A shorter program is usually better than a longer one, but a short program that does not compute the right answer is worth much less than a longer program that computes the correct information.
• Test your program with the simulator
• There are several possible approaches. My main criterion for this problem is for your program to compute the correct answers, but it will make me especially happy to see imaginative and elegant solutions.

Submission

• Follow the same steps as in Problem 2, but this time enter 3 in the Problem number box.

Submission

• Submit your answers on sheets of paper that should have your name on each one.
• Staple all the sheets of paper together, please!

Problem #4 (Optional and Extra Credits)

If you solve this problem, submit your code electronically, as for the previous 2 problems.

• First, read the section on Indirect Addressing in this document.
• Then play with the program below that uses indirect addressing with the sto-i instruction:

start: 
	lod-c table	; get address of table in AC
	sto   loc	; store it in loc variable.  Now loc
			; contains the address of the first memory cell
                	; starting at table.
loop:
	lod    counter	; get counter in AC
	sto-i  loc	; store AC at address contained in loc variable

	inc		; increment AC
	sto    counter	; store back in counter.  Now counter is greater by 1

	lod    loc	; increment loc variable to "point" to next 
	inc		; memory cell in RAM.
	sto    loc

	lod    counter   ; get counter back
	sub-c  11 	 ; subtract 11 from counter
	jmz    done	 ; if AC is 0, then counter was 11.  We can stop.
	
	jmp    loop	 ; otherwise, we loop back

done:
	hlt

; data section
;
table:   0
         0
         0
         0
         0
         0
         0
         0
         0
         0
loc:     0
counter: 1

• Read the comments. See if they make sense. Try to figure out just by reading the program if you can tell what it's doing. You need to understand the indirect addressing property of sto-i to fully see what is going on, so make sure to read and understand that section of the document indicated earlier.
• Run the program. Notice that it will store all the numbers from 1 to 10 in the 10 memory words starting with the variable table. Below is an example of the memory contents once the program has finished running:

Your Assignment

Your assignment for this optional and extra-credit part is to modify the program so that instead of storing the numbers 1 to 10 in memory, it computes and stores the numbers 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512 in memory.

Below is an image of what the memory of my solution program looks like once it has finished executing. Your data section should look similar, especially the numbers 1, 2, 4, ... 512 in successive memory words.

Submission

Follow the same steps as the programs for Problems 2 and 3, but enter 4 in the Problem Number box.

...