[Nebullis]

And who cares whether it's binary or base 256?

I wasn't referring to 'base'. I was referring to state. A bitflip mutation program requires a system of two states such as software uses. And, yes, you can find multiple bitflip paths between DOS and Windows XP.

[maro]

I think you are very confused. Current computer hardware relies on base 2. Base 2 is implemented physically as two STATES--high voltage and low voltage. From the applied math point of view, we are dealing with base 2, regardless of the implementation method. The intrinsic base 2 design of the hardware is used to represent numbers in hexadecimal, or base 16. From the machine level hex representation, other layers of software represent numbers to the users in base 10, which is the way most people represent numbers. So what? If our hardware was configured as base 4 using four distinguishable voltage states, nothing about our computer technology would change. Nothing that mathematicians do is base-dependent. That is a stunningly obvious statement--or so I thought before I read your comments. The set of integers does not assume any particular representation of integers. As far as your strange statement that there is a path from DOS to XP--do you mean that there is a progression , DOS1, DOS2, DOS3...DOSN, where DOSN is XP, where each element in the progression differs from the last by a few bitflip changes, and each intermediate program is a working program? If you do, you are quite wrong, and have never written any software.