The Know-how Computer

The Know-how Computer is a simple pen-and-paper computer that was developed by Wolfgang Back and Ulrich Rohdein in the early 80's to help educate people on basic computing and assembly programming.

Setup

Materials

Preparation

You should now have something that looks something like this:

Line Code Register Value
0 R0
1 R1
2 R2
3 R3
4
5
6
7
...

Instructions

Before we get started, we need to learn some instructions. These are some of the most basic instructions in machine code and assembly and with these, you technically could compute anything as it's Turing complete (as long as you have a LOT of paper and a LOT of time).

Instruction Meaning
JMP n Jump to line n
INC Rn Increment the value in register n
DEC Rn Decrement the value in register n
ISZ Rn If the number in register n is zero, execute the next instruction. Else, skip the next instruction.
END Stop the execution of code and end the program.

Usage

First Program

For the most basic example, lets write a program that will decrement a register (DEC) until it reaches zero (ISZ), where we will end the program (END). We will assume that R0 has 3 in it, represented by 3 of whatever you are using. Lets start by writing it in plain English:

Now that we have this and have run through this in our head to ensure it works, we can put this into our instructions for our paper computer:

Line Instruction
0 ISZ R0
1 END
2 DEC R0
3 JMP 0

Start with a number of enumerables in R0 and go from line 0, using your pen as a pointer to which line you are currently on. Starting this program with any number will result in a constant decrementing until R0 reaches zero, where the program will end. Try it!

Addition

This is where things will get a little trickier to conceptualize. We will start with two values in different registers (R0 and R1) and add them together into a single register. This will take a little more breaking down before we can turn it into code.

Instead of being able to just move all of our enumerables from one register to another, we actually need to convert this into multiple instructions, since we don't have an instruction like ADD to make things easy. What is another way we can think of taking one thing from one register and putting it into another?

So now that we've translated addition into language that our code can adapt to, lets finish by putting our whole program in plain English again, assuming that we are adding R0 and R1 together, with the result of our addition residing in R1:

These are now all much simpler to translate back into our instruction set:

Line Instruction
0 ISZ R0
1 END
2 DEC R0
3 INC R1
4 JMP 0

Now go ahead and try this with your paper computer, again putting any number of enumerables in R0 and R1 and using your pen as a pointer for the current line.

Challenges

With these challenges, you may need to extend the amount of lines and registers you have available. Don't be afraid to use as much as you need and streamline it later!

  1. Make a program that subtracts one number from another and completes with the difference in one register.
  2. Make a program that multiplies two numbers together and completes with the product in one register.
  3. Make a program that divides two numbers and completes with the quotient in one register and the remainder in another.

Solutions

This subtracts R0 from R1, so R1 must be larger than R0.

Line Instruction
0 ISZ R1
1 END
2 DEC R0
3 DEC R1
4 JMP 0

This multiplies the numbers in R0 and R1 together, placing the resulting product in R2.

Line Instruction
0 ISZ R1
1 END
2 DEC R1
3 ISZ R3
4 JMP 8
5 DEC R3
6 INC R0
7 JMP 3
8 ISZ R0
9 JMP 0
10 DEC R0
11 INC R2
12 INC R3
13 JMP 8

This divides the number in R0 by the number in R1, placing the quotient in R2 and the remainder in R3.

Line Instruction
0 ISZ R1
1 END
2 ISZ R0
3 END
4 ISZ R1
5 JMP 10
6 DEC R0
7 DEC R1
8 INC R3
9 JMP 2
10 INC R2
11 ISZ R3
12 JMP 2
13 DEC R3
14 INC R1
13 JMP 11

References

  1. https://en.wikipedia.org/wiki/WDR_paper_computer
  2. https://www.youtube.com/watch?v=Z27KQiBnkJI
  3. https://wiki.xxiivv.com/site/papier.html

Last modified: 202109262227