Pushing BUTTONS

BUTTONS is a tiny computer that you can program entirely with a 2 button mouse by clicking on buttons. It features all of the operations you need to learn about computers and how they process numbers. All you need to do is click on the right buttons and make BUTTONS do the math.

Stacking Plates

Imagine if I handed you a stack of dinner plates and told you to number each one. I give you a grease pen and a STACK of 10 plates and tell you to get to work. How would you number these plates? When you were done how would the plates be stacked? Let's call the unnumbered plates new plates and your stack of numbered plates done plates.

You would probably take the first plate off the top of the stack of new plates, write the number 1 on it, and then set it to the side in the done plates stack. You can't put it back on the new plates stack of plates because then you wouldn't make your way through the plates. You take one off the top of the new plates, write the number 2, and put it on top of the stack of plates called done plates. You then do this with #3, #4, #5, until you are done going through all 10 plates.

You then look over at your stack of numbered done plates and you're happy, but the plate on top is numbered 10. You've stacked them in reverse, and you probably need to re-stack them in order. How would you do that? Well, you simply take one off the top of the done stack and put it onto another stack (let's call that sorted) until you're out of plates. Now sorted stack is numbered 1-10, with 1 on top.

Try this with 10 pieces of paper instead of dinner plates. Cut up 10 little cards that do not have numbers on them, and then write the numbers 1-10 on each piece of paper and stack it just like above. Then restack them again to get them in the sorted order. This is a stack and it's used in computers and in BUTTONS.

PUSH & POP

The way BUTTONS remembers what it's doing is with a STACK. A STACK is a very simple storage system that takes numbers one at a time and puts them on top of each other, just like with the dinner plates in the previous explanation. Numbers are pushed onto BUTTONS' version of a STACK and the last one in is the first one out.

You should go get a note book and write these things down. Be sure to write, "A stack is a last in, first out number storage. The last number I push onto the stack is the first number to come out." I say this because I actually got this wrong in the first implementation of the stack, so if I can get it wrong, so can you.

You PUSH numbers onto the STACK, then call other operations (ADD for example) to make BUTTONS do math on them. When you PUSH you have to give it the number it should push onto the top of the STACK. On the right you'll then see BUTTONS show that number under the STACK output.

The POP operation simple takes any number that's on the top of the STACK and removes it. Junks it. Throws it away. If you try to POP too much your BUTTONS will crash. Don't do that.

Math

You can now PUSH numbers onto the STACK and use POP to take them off. Big deal. That's not a computer...yet. The next piece of our puzzle game is to let you do math with these numbers on the STACK. BUTTONS has the following simple operations:

The order of each operation is the same, with a being PUSH on first, then b. That means when you're done your b number should be on the top of the STACK. Here's how I would add 1 + 2:

0: PUSH 1
1: PUSH 2
2: ADD

When you run these lines of code in BUTTONS the number 3 will be at the top of the stack ready to use. You can also try POP to remove it and see how that works.

When you see the 0: at the front of the line that's the line number. It's not code, just me being lazy and not wanting to implement line numbers in fancy CSS.

CLICKS

Before we get into loops I have to warn you that BUTTONS is not a very powerful computer. It can only perform 256 operations before it runs out of energy called CLICKS. If your program runs for 256 many clicks then BUTTONS will stop running and give up because it is tired.

Looping with JUMP

To make a computer we need a way to repeatedly run code so we can do many calculations. BUTTONS has the operation JUMP that will jump to the line you give, then keep running. If I want to run a loop that counts from 1 to 256 I can do this in BUTTONS:

0: PUSH 1
1: PUSH 1
2: ADD
3: JUMP 1

You really should study this simple little program because inside it's simplicity is an incredibly powerful idea. Here's some questions to ask while you study:

1. Why do I do JUMP 1 instead of JUMP 2 to reach the second line?
2. Step through the code and write down what the top of the stack is at each step.
3. If you want to go up by a different count what do you do?
4. How does this work with SUB, DIV, MUL, and MOD operations?

Play with this code in BUTTONS until you understand what's going on because if you don't get JUMP then you definitely won't understand the next section.

You can also JUMP one line past the end of your code to end your program. That means if you have 4 lines of code, then you can do JUMP 5 and end your program. This becomes important later so write this down in your notebook too.

Logic with JZ/JNZ

You now know how to make BUTTONS do math, use the STACK, and do a loop to do lots of math. There's one last thing we need before we have a real working computer and that's the idea of a test and jumping only if that test is true (or false).

Let's say you have the following code that counts down from 10 to 0:

0: PUSH 10
1: PUSH 1
2: SUB
3: JUMP 1

You run it, thinking it will stop at zero, and instead BUTTONS does exactly what you told it to do and keeps going until it runs out of CLICKS, leaving .... -32 on the top? What?!

The reason is you have no way to tell BUTTONS when to stop. You can tell it to do the math and where to JUMP but you have no way to tell buttons "when you reach 0 on the STACK you should stop." You do this with the JZ operation which means "JUMP if Zero". It simply looks at the top of the STACK and if that's 0 then it does a JUMP to where you want. This is doing a test of the top of stack, and a jump. Now we can rewrite our program like this:

0: PUSH 10
1: PUSH 1
2: SUB
3: JZ 5
4: JUMP 1

See how line 3 is now JZ 5, but right after that on line 4 we have JUMP 1? This seems very backwards, but we have to do this because we want line 3 to only JUMP 1 to the end (line 5 is the end) when the STACK is 0. It's working as a "guard" that prevents line 4 JUMP 1 from running when the STACK is 0. Another way to see this is it will "jump over" line 4 JUMP 1 when the STACK is 0.

We can simplify this by using another operation called JNZ which does the inverse of JZ and "jumps if NOT zero". Using this operation we can now have:

0: PUSH 10
1: PUSH 1
2: SUB
3: JNZ 1

Instead of that weird "jump over the next line that's a jump if the stack is zero" in the previous program, we have "jump to line 1 if stack is not zero". Way easier to do, but keep in mind you many times need both. Both effectively do the same thing but it's sometimes easier to use one or the other (JZ vs. JNZ) depending on how you're doing the operation.

STOR/RSTOR Registers

You technically can do all of the computation you need with just that (minus input and output), but it's really annoying and hard to do much more than add some numbers in loops. To make it possible to implement larger more complex prgrams in BUTTONS you have four REGISTERS where you can keep temporary variables for later: AX, BX, CX, DX, IX. I named them this way just for old time's sake, and to keep things simple. You put things into these registers (and take them out) using the STOR and RSTOR (for "restore") operations:

The IX register is special when used with PEEK and POKE to access RAM. The IX register will work like all of the others, but with PEEK and POKE it will automatically be incremented by a number you give those operations. See below in the section on RAM for more information.

Let's say I want to count down like before, but I want to keep track of the previous number as you go. I don't know why. You just do. Ok, here's how:

0: PUSH 10
1: STOR AX
2: PUSH 1
3: SUB
4: JNZ 1

Now as you step through this program you can watch the AX register keep the previous stack top as it goes. Let's say you want to keep the initial value you started with for after the loop:

0: PUSH 10
1: STOR AX
2: PUSH 1
3: SUB
4: JNZ 2
5: RSTOR AX

Now I do JNZ 2 instead so that I avoid the 01: STOR AX line, that does the loop like before but now the AX register has my starting number. After line 4: JNZ 2 passes I then use RSTOR AX to get that number back, and the program ends with two numbers on the stack: 10 and 0.

Other Operations

You can also use these operations to do other things:

RAM with PEEK/POKE

You have 64 cells of Random Access Memory (RAM) to store numbers into. You can think of RAM like an spreadsheet that you can put any number you want into at random in each cell. The only catch is you have 64 cells to work with, and you have to "address" them by a single number from 0 to 63.

The POKE is used to write to RAM and works as follows:

1. Takes a single number for the increment: POKE 1
2. It then takes the number that's currently on the top of the STACK,
3. The address in IX,
4. Then writes the STACK top number into RAM address given by IX.
5. Finally, it take the increment from #1 and adds that number to the IX register.
6. One more thing: The IX register is only big enough to store 0-63, and will wrap around if it goes past this. This means if you go past 63 it should wrap around to 0 again, assuming you're looping by 1.
7. STACK After the PEEK the stack is unchanged.

That's a lot to deal with, but let's look at the PEEK operation does the same thing just in reverse:

1. Takes a single increment: PEEK 1
2. Takes the address in IX.
3. Reads the address in RAM that IX gives.
4. PUSH the number from the RAM address onto the STACK.
5. Finally, increments the IX register by the number given in #1.

PEEK and POKE Example

Here is an example that just fills RAM until BUTTONS runs out of CLICKS:

PUSH 0
PUSH 1
ADD
POKE 1
JUMP 1

Here's a more complete example that counts from -10 to 0, putting each number into RAM, then goes back through and puts each one on the stack one at a time.

PUSH -10
PUSH 1
ADD      
POKE 1
JNZ 1
STOR IX
POP
PEEK 1
JNZ 6