How would that work? O.o There'd be only one command, wouldn't there?

You know, we always talk about how NOP is a useless instruction, but actually, ld a, a etc. are the only useless instructions on the z80.  NOP DOES have its purposes

Use zeros... And spaces?

actually, it involves counting the numbers of 0s.

think tally marks, minus the 5 groupings. That's unary. Binary allows having ones separating the zeros, but unary doesn't, so (I'm representing the bits as one for clarity) 111111 = 1+1+1+1+1+1 = 6 , or command #6.

As such, it's easy to make a binary processor pretend to be unary, just as a quaternary one can easily pretend to be binary.

@epic7 zeros and spaces would be two symbols, and therefore binary.

An 8 bit CPU would have 9 possible states: {},{1},{11},{111},{1111},{11111},{111111},{1111111},{11111111}

and each wire would be powered after the previous, so it's easy to convert from an analog voltage by using compariters.

Binary is much better, of course. quaternary is better than binary in the same way.

That wouldn't work. Memory has to be initialized to some set of states, so unary is impossible. Let's take a look:

Let's say we have a turing machine where all the cells on the tape can hold a unary 1 and that's it (it's unary, remember). Now, the machine looks at the first step and sees a 1. So, does it read that as {1} or {11} or {111} or any of the other possible combinations? Let's say it decides based on some magic oracle that it's not {1}, so it looks at the next cell and sees another 1. That narrows the choice down to {11}, {111} and so on. There is no way on the basis of the information provided in the memory tape to distinguish between the opcodes. The machine can have at most one instruction and since memory cannot be modified (unary memory sucks), it can't possibly be Turing complete. Basically, an Unary computer can execute any one instruction repetitively so long as that instruction is trivial (e.g. a NOP or outputting a constant value on a line).

That's not an unary computer. That's a binary computer with unary opcodes.

Indeed, it is impossible to program using *only* 0's without using something like grouping.  This however adds in more information than just the 0's themselves provide, so you are not using *only* 0's

Did you know that the vast majority of RAM already relies on higher-base storage concepts? Yet, it is part of a binary computer system.

That's because the fundamental unit of information is the bit, which coincidentally, is the same unit used in binary Notice that the bit contains more information than a unary digit. As Builderboy said (and you implied with the statement that "it has to read them all until it reaches a zero"), with *ONLY* 0's, you can't build a computer using unary instead of binary. There just isn't enough information in unary digits by themselves to determine multiple opcodes. Additional information in the form of formatting is inherently necessary.