One format I've seen in several places (the MIDI file format, for example) is base-128 with the high bit set on all bytes except the last, i.e. (in hex):

0 = 00
1 = 01
...
127 = 7F
128 = 81 00
129 = 81 01
...
255 = 81 7F
256 = 82 00
...
16383 = FF 7F
16384 = 81 80 00
...

The nice thing about this is a number always encodes to a multiple of 8 bits - reading and writing data tends to be much easier when everything is byte-aligned.

I don't think this AI-Singularity narrative, that seems to be getting so popular, is actually possible. First, there can be no such thing as an "artificial general intelligence" - it's long been known that there are classes of logic problems which no algorithm can ever solve arbitrary instances of, such as the halting problem.

More importantly, no mind (whether human or artificial) can ever intentionally design an AI smarter than itself. If I could design an AI smarter than me - smarter in that its mental algorithms can solve some problem P while mine cannot - then:

• I would have to be able to understand that AI's reasoning process, and why it works (if I just write code without understanding what it actually does, there's little hope of it working)
• I would be able to follow that process through a debugger as the AI tackles P
• I would thus be able to understand the solution of P and be convinced that it is correct

But that would mean I'm already capable of solving P myself - because I never really had to program the AI at all to do any of that; I could have just simulated it with my own brain plus a lot of pencil and paper (albeit much more slowly). Contradiction.

We can only design AIs to do things more quickly that we can already do... and accelerated stupidity is not an existential threat.