In "A New Kind of Science" Stephen Wolfram states that a computer can be built with only two commands:

Increment x

Decrement x, jump when x = 0

I spent some time thinking about this.

Imagine a hypothetical machine with three registers AX, BX, CX . Provide it with a register DX which serves only as the output buffer for any imaginary output device. Also provide it with a fourth register ZX which always equals zero.

Assumeing that dec can jump to a poistion specified by, say CX  then I was able to derive the four basic operations of mathematics:

Add:

Subtract:

Multiply:

Divide:

I can't claim these are elegant algorthims.

Can anyone send me tighter code?

Defination:

inc a

dec a , b  where b contains the address to jump to if a proves empty. I am also assumeing that the opcode functions as:

{

if a = 0 then goto b else

a = a - 1

}

So if a contains 1, then 1 will be subtracted, and a jump not executed.

I have no idea why I assumed this behavior. Changeing dec a,b to the function

{         

a=a-1

if a = 0 then goto b

} 

will naturally derive different behavior.

Example multiply:

It is my nature to combine obsessions.

The IMISet provides a simple framework for the archetecture of my Marble Calculater.

See Physical Counter Computing