My mistake, I meant **3 bits is one zero in a ordinary number**. 10 bits, is 3 bytes. 1GB of 1s & 0s in binary can store sooooo many entities. Image 10 bits. **10 bits is really 1,000**. Now imagine 1,000 entities - 000000000000000000000000000000000000000000000000................. Now images what not 10 bits is, but 800,000,000,000 bits is!

The 9^9=n was about **using very little bits to make a big number**. I want to make 10MB into 100 bytes, 9^9 ^ 9 ^ 9 ^ 9 ^ 9 can generate a number so big we can't even run the calculation. Unfornunately I don't know how to control it enough. So many big results, so few starter bits, not possible really.....but for some cases, yes! I can generate a huge movie using a few bits. Imagine that!

I think you may be confusing

**binary **and

**decimal** - and something more. A byte is not a decimal digit, but 8 binary digits.

The fact that we can store 1000 in 10 bits means that, for example, the decimal ("ordinary") number 1000, written in binary, is 1 111 101 000, which takes 10 bits (binary digits). With ten bits, you can store any of 1024 different numbers (one at a time, of course).

What you apparently mean by "3 bits is one zero" is that each digit in a decimal number (that is, each factor of 10) corresponds to about 3 bits. As we've said, 3 bits actually holds 8 numbers (0 through 7: 000, 001, 010, 011, 100, 101, 110, 111), so you're slightly overestimating it.

But the rest of what you're saying makes no sense at all, in terms of what bits actually mean.

Your second paragraph suggests that

**you aren't thinking of number systems and bytes and bits at all**, but about a very different challenge: how large a number can you express using a given small number of

**characters **in a mathematical expression; or, conversely, how few symbols can you use to express a given large number (which is a much harder challenge). Yes, some special numbers can be obtained very compactly, but that doesn't mean that any given number can - for exactly the reason we've been discussing.

Sometimes we see discussions about what is the largest number you can "write with three digits". They will say 9^(9^9); but depending on the rules of the game, 9!^(9!^9!) is much bigger, and you can go far higher than that. But that's just a silly puzzle, not something interesting about actually representing numbers in general. Most numbers can't be written so compactly.

Am I guessing correctly what you have in mind?