Little Man Computer, How to multiply?

Multiplication is a type of addition. 6*7 = 7+7+7+7+7+7

Follow the approach given below:

1. Branch it out.
2. Load first no.
3. Load second no.
4. Compare second no from 1 till its value.
5. End Branch once done.

Hope this logic helps you.

Ok so given the options I have how would my commands go?

Using Branch, are you able to loop through a given condition.
Since you have three types of Branch statements, I believe atleast one of them should work for loop statements.

If you have loop then you can write a looping condition to achieve your output right.

Do you need to be able to handle one or two factors negative? Or at least equal to 0? If so, a few more subcases need to be considered...

No only positive.

I have found out that the BRANCHZ can be used as a loop. So given this information how would this go if you were to put all of the functions in order?

Ok here is what I have so far but it's not working out so far. What am I doing wrong? HELP !!!!!!

Line#     Instruction     Address
00          READ        
01              STORE         60
02              READ        
03              STORE         61
04          BRANCHZ   60
05              PRINT
06              STOP

Ok. Here's the logic:

1. READ and STORE first value as 60.
2. READ and STORE second value as 61.
3. STORE third value as 1.
4. BRANCHZ first value till third value equals first value.
5. ADD second value with second value and STORE.
6  ADD 1 to third value and BRANCHZ it.

Hope this solves. If you get any errors in logic give me the parameters accepted for those keywords so that I can think more deeper.

I tried this logic out but had problems.
I tried the following

READ
STORE 60
READ
STORE 61
BRANCHZ 60
BRANCHZ 60
BRANCHZ 60
BRANCHZ 60
ADD 61
STORE 62
ADD 62
BRANCHZ 62
PRINT
STOP

When it got to the first BRANCHZ I get the following error message Referring to address with no instruction

hiya... i did some 6502 stuff some years ago so this is pretty closely related. hope it's what you're looking for.

start                      // multiply two numbers
                           // written by paul tomasi 2/2008
 
                           // get two numbers
							
get1     READ              // get number from user
         BRANCHZ get1      // if it's '0' get another
         STORE num1        // store as num1
 
get2     READ              // same process for num2
         BRANCHZ get2
         STORE num2
 
                           // swap num1 with num2 to optimize for smallest countdown
							
         SUBTRACT num1     // subtract num1 from num2 
         BRANCHP swap      // if positive result num2 is greater than num1
		
                           // initialise count and running total (num2)
							
         LOAD num2	         // initialise count with smaller number
         STORE count
         LOAD #0           // reset running total
         STORE num2
         BRANCH loop       // go and multiply
 
                           // swap num1 and num2 so num1 = largest number
							
swap     LOAD num1	         // initialise count with smallest number
         STORE count
         LOAD num2	         // move largest number into num1
         STORE num1
         LOAD #0           // reset running total
         STORE num2
 
loop     LOAD num2         // add number to itself and store
         ADD num1
         STORE num2
         LOAD count        // countdown (using smaller number of the two)
         SUBTRACT #1
         BRANCHZ exit      // if no more to do, exit loop otherwise...
         STORE count       // store count and repeat loop
         BRANCH loop
 
exit     LOAD num2         // get result (running total)
         PRINT             // output it to user
         STOP              // end
 
                           // data section
							
data     num1
         num2
         count

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here's a slightly modified version.

the code for reseting the running total need only appear once - as we can jump to it before multiplying. this is also neat because after the swap routine,we run into it anyway.

start                      // multiply two numbers
                           // written by paul tomasi 2/2008
 
                           // get two numbers
							
get1     READ              // get number from user
         BRANCHZ get1      // if it's '0' get another
         STORE num1        // store as num1
 
get2     READ              // same process for num2
         BRANCHZ get2
         STORE num2
 
                           // swap num1 with num2 to optimize for smallest countdown
							
         SUBTRACT num1     // subtract num1 from num2 
         BRANCHP swap      // if positive result num2 is greater than num1
		
                           // initialise count and running total (num2)
							
         LOAD num2	         // initialise count with smaller number
         STORE count
         BRANCH multiply   // go and multiply
 
                           // swap num1 and num2 so num1 = largest number
							
swap     LOAD num1	         // initialise count with smallest number
         STORE count
         LOAD num2	         // move largest number into num1
         STORE num1
		 
multiply LOAD #0           // reset running total
         STORE num2
		 
loop     LOAD num2         // add number to itself and store
         ADD num1
         STORE num2
         LOAD count        // countdown (using smaller number of the two)
         SUBTRACT #1
         BRANCHZ exit      // if no more to do, exit loop otherwise...
         STORE count       // store count and repeat loop
         BRANCH loop
 
exit     LOAD num2         // get result (running total)
         PRINT             // output it to user
         STOP              // end
 
                           // data section
							
data     num1
         num2
         count

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and if you're interested, i've included a MS-DOS batch file simulation which you can run from a DOS command line.

Copy and paste the code straight into notepad and save as MULTIPLY.BAT the just run it by typing:

   MULTIPLY

at the DOS command prompt

PS. Runs in XP
 

@rem multiply.bat
@rem written by paul tomasi
@rem simulates assembly code to multiply two numbers
@echo off
 
:start
:get1
set /p Acc=#1 
if %Acc% EQU 0 goto :get1
set /a num1=%Acc%
 
:get2
set /p Acc=#2 
if %Acc% EQU 0 goto :get2
set /a num2=%Acc%
 
set /a Acc-=%num1%
if %Acc% GTR 0 goto :swap
set /a Acc=%num2%
set /a count=%Acc%
set /a Acc=0
set /a num2=%Acc%
goto :loop
 
:swap
set /a Acc=%num1%
set /a count=%Acc%
set /a Acc=%num2%
set /a num1=%Acc%
set /a Acc=0
set /a num2=%Acc%
 
:loop
set /a Acc=%num2%
set /a Acc+=%num1%
set /a num2=%Acc%
set /a Acc=%count%
set /a Acc-=1
if %Acc% EQU 0 goto :result
set /a count=%Acc%
goto :loop
 
:result
set /a Acc=%num2%
echo Result [[%Acc%]]
 
:end
set num1=
set num2=
set count=
set Acc=
 
exit /b

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Try this...The logic should be like

READ
STORE 60
READ
STORE 61
BRANCHZ 60
BRANCHZ 60
BRANCHZ 60
BRANCHZ 60
ADD 61
STORE 59 -- (60-1)
ADD 61
BRANCHZ 59
PRINT
STOP

Having revisited this question, I have looked deeper into LMC and found the following link which has a java-based LMC simulator.

http://www.atkinson.yorku.ca/~sychen/research/LMC/LMCHome.html
http://www.atkinson.yorku.ca/~sychen/research/LMC/LittleMan.html

Looking at the small instruction set, I was able to write code after just a few moments. The following code is based on their instruction set however, I have also translated this using the instructions you have provided above.

   INP
   STA 16
   INP
   STA 17
   LDA 17
   BRZ 12
   SUB 15
   STA 17
   LDA 18
   ADD 16
   STA 18
   BRA 4
   LDA 18
   OUT
   HLT
   DAT 1
   DAT 0
   DAT 0
   DAT 0

As you can see, there are four data locations: 15 is preset to the value '1' and is the value subtracted from our count during each iteration of the loop. 16 contains the first inputted number. 17 contains the second inputted number which acts as a countdown to zero. Finally, 18 is the running total where the result is stored during each iteration and from where we fetch our result at the end of the program.

This translates to the following machine code which can be entered directly into the LMC simulator. Then, by clicking the 'Step' button, you'll be able to see each instruction processed step-by-step.

   901
   316
   901
   317
   517
   712
   215
   317
   518
   116
   318
   604
   518
   902
   000
   1
   0
   0
   0

Using the instruction set you have provided yourself, this would translate to:

   READ
   STOREA 16
   READ
   STOREA 17
   LOAD 17
   BRANCHZ 12
   SUBTRACT 15
   STOREA 17
   LOAD 18
   ADD 16
   STOREA 18
   BRANCH 4
   LOAD 18
   PRINT
   STOP
   1
   0
   0
   0

Explanation:

The first four lines are straight forward.

   READ    -    get 1st number into A (Accumulator)
   STOREA 16    -    store it in memory loaction 16
   READ    -    get 2nd number into A
   STOREA 17    -    store is in memory location 17. This will be our countdown value

Next, we start our loop:

   LOAD 17    -    get the countdown value from memory location 17
   BRANCHZ 12    -    if it has reached zero then jump out of the loop, otherwise....
   SUBTRACT 15    -    subtract the number stored in location 15 (which is preset to '1'), and....
   STOREA 17    -    store the value back in memory location 17

That completes the conditional loop control

   LOAD 18    -    get our running total into A (first time loaded this will be zero)
   ADD 16    -    add the first number to it, and....
   STOREA 18    -    store it away again

So, this is basically adding the first number to itself for as many times euqal to the value of the second number

   BRANCH 4    -    go back to memory location 4 which is the start of our loop and repeat the process

And that completes the loop. Going back to our 6th instruction, this was a branch if zero to exit the loop, and this brings us here (memory location 12).

   LOAD 18    -    get our running total into A, and....
   PRINT    -    display it as our result

Finally, we must terminate the program otherwise it will run into our data section and do some silly stuff.

   STOP

And that's all there is to it.

The program starts at memory location 0 and occupies only 15 memory locations. The 16th memory location (15) is the start of our data. Memory location 15 is pre-set to '1' and is used to decrement our 'count' value. 16 is where our first number is stroed. 17 is where our second number is stored and is subsequently used as a countdown-to-zero to count how many times we should add the first number to itself (simple multiplication). 18 is where we store our running total - the result.

I hope this is clearer for you.

If you have further problems please let me know which LMC program your instructions belong to or provide a link to where you got your mnemonics from.

Just to make sure you got it....

00   READ
01   STOREA 16
02   READ
03   STOREA 17
04   LOAD 17
05   BRANCHZ 12
06   SUBTRACT 15
07   STOREA 17
08   LOAD 18
09   ADD 16
10   STOREA 18
11   BRANCH 4
12   LOAD 18
13   PRINT
14   STOP

15   1
16   0
17   0
18   0

t0t0 this explanation is great and I think is getting close. I tried this out and I get the following error message when I get to the 7th step down. Also LMC didn't like it the first time I tried using STOREA so I used STORE instead. That got me to the SUBTRACT 15. This is when I received the following error message.

Error: Instruction subtract, "garbage loaded on address 15"

How do I preset address 15 to 1? Maybe this is why I get the error message.

Check out the looping logic in the same site as mentioned earlier.

http://www.atkinson.yorku.ca/~sychen/research/LMC/LMCLoops.html

There are some more additional commands present in Little computer it seems as per the site. Try using those too.

Just type a '1' in location 15.

Could you tell me what program / simulator / emuolator you're using so that I can synchronise with you.

If it's the LMC I gave you a link to earlier then just type a '1' in location 15. Also, type a '0' in locations 16, 17 and 18 as well - although these will probably be zero to start with anyway.

I wasn't sure about your STORE and STOREA but because LMC appears to operate on the Accumulator I assumed we should use STOREA.

rrjegan17

the link you posted above is unrelated to this question as the loop employed in this application need only count down to zero so we're anly testing for zero.

when you load a value into the Accumulator a single instruction ie, BRZ is enough to perform the loop's conditional statement whereas, in the example you provided a 'count' value is loaded then '10' is subtracted from it and then tested to see if the result is positive - a bit messy for our needs.

t0t0 it is Assembler Visual Builder version 1.0.2. I have attached a screen shot.
LMC.jpg

Ok.. Thanks for the snapshot.
I havent used it or seen it earlier.

stonebreaker

Sorry, I've been out for the day in the snow with my little one.

Right, I have two solutions for you which I will discuss in detail as soon as I have completed my write-up.

In the meantime, if you want to crack on with one of my solutions have a look at the following code. This WILL need some explanation so that you understand sometimes not everything is done using conventional methods because in assembly language, we can get away with the 'unconventional'.

Using the (rather uninspiring) LMC interpretter (of your choice), enter the code and click the 'Compile' button. Before stepping through the program, grab the right-hand scrollbar and drag it down so that you can see the memory range 36..39. When stepping thrpigh the program, you can observe the values changing (most notably 36 and 37). The result is displayed in the 'Output Stream' wndow.

00  LOAD            09  =  109
01  SUBTRACT   13  =  413
02  STORE          39  =  239
03  READ                  =  901
04  STORE          38  =  238
05  READ                  =  901
06  STORE          37  =  237
07  LOAD            19  =  119
08  STORE          36  =  236
09  LOAD            37  =  137
10  BRANCHZ     17  =  617
11  SUBTRACT   39  =  439
12  STORE          37  =  237
13  LOAD            36  =  136
14  ADD              38  =  338
15  STORE          36  =  236
16  BRANCH       09  =  509
17  LOAD            36  =  136
18  PRINT                  =  902
19  STOP                  =  000

You have done it!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Thank you so much for all of your help. I look forward to your explanation so that I can learn and understand it better. Once again thank you so much.

My explanation is almost complete.... I will post it in about 30 minutes or so.... please bear with me

stonebreaker

Thank you for  accepting my solution. I don't know what your knowledge of assembly programming is but I wonder, did I make things clear enough for you to understand what was going on?