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.

Misc. Information

If you haven't already read it, there is a lot of good information in the Introdcution to the xComputer document.

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: 100
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 us (microsecond).
• 0.000000001 sec = 1 ns (nanosecond).

Problem #2

You need to submit a printed version of the program for this question

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.

Copy/paste a copy of your program in your favorite editor or word-processor and print a copy of it for submission.

Problem #3

You need to submit a printed version of the program for this question

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, although I am more interested in your program computing the correct result than in how short they are.
• 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

• 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)

• 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 it stores the first 10 powers of 2 in memory, i.e. the numbers 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512.

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

If you decided to solve this problem, then submit a typed listing of your program with the other answers to Problems 1 to 3.