A new way to store data

I've always been fascinated by how
a number can exist in different
numbers systems, or bases. The
binary number system, is how
computers store and transfer data.
This is because it only requires
two digits, 1 or 0. They can be
represented by two states- on and
off. Because building a powerful
analog computer is tricky, this is the
only suitable number system.
But this wastes a lot of space, as
I will demonstrate shortly. Because
Binary has only two digits, representing
three-digit decimal numbers can take
several bits (binary digits).

(27)₁₀ = (11101)₂ 
(500)₁₀ = (111110011)₂


So, you can imagine, that since
computers use numbers in the millions
and the billions, using a system like
Base 10, would result in a huge storage
solution. Previously full hard-disks, could
become nearly empty.

Now, I recently came across a riddle,
which might hold the solution to this
problem. The riddle went something like
this-

You have a weighing scale, with two
pans on each end. What is the least
number of weights you have to use to
weigh every number from 1-8?

The answer, would be obvious to
anyone who is very familiar with binary.
You need all the powers of two, which are
smaller than, or equal to 8- 1, 2, 4, 8. So,
the answer is 4. You can try it for yourself.

But, there is a cleverer answer. Since there
are two weighing pans, you can also subtract
weights. So, the new answer becomes 1, 3, 9.
You only need three to do the job.

1 = 1
2 = 3 - 1
3 = 3
4 = 1 + 3
5 = 9 - 3 - 1
6 = 9 - 3
7 = 9 - 3 + 1
8 = 9 - 1

This could then result in a new way to store and
transfer data. If there were a way to mark digits as
negative, then it would represent an innovation in
the field of data storage.