Quarter Imaginary Number System

There are 10 kinds of people in the world. Those who know binary and those who don't.

In case you have never seen this joke before and you don't know what I'm talking about:

The decimal number system, is the most common numbers system used by people today.
I think the Sumerians liked 60gesimal number systems.
we like the decimal system because having 10 fingers it's easy for us to count when we learn arithmetic. If you have good memory or really bad math skills you'll remember the last time you used your fingers to aid yourself in calculation.

The way the number system works is the adoption of ten arbitrary symbols to represent the digits one having greater value than the next by a singular unit which is the first digit

therefore 0 is the first digit 1 is the succesor of 0 (S0), 2 is the succesor of 1 S1 (SS0), 3 = SSS0, 4=SSSS0, 5=SSSSS0,6=SSSSSS0, 7=SSSSSSS0, 8=SSSSSSSS0,9=SSSSSSSSS0.
when you reach the end of the scale or when you need to represent S9 the system places the smallest unit in the following 'space' so 10=S9 and 11=S10 and so on.
to expand from other number systems to decimal the value of the second 'digit' with the minimal input is considered the base and an expansion in the following manner is computed.
XYZ=X*B^2+Y*B+Z*B^0 usually the digits XYZ... may not exceed the base so as to avoid two possible ways to represent the same number (non-uniqueness )

Binary only uses the digits 1,0 actually they are called bits when binary is referred to.
therefore 10 in binary is 2 in decimal (1*2+0*1).

THE COOL THING IS
that you can make your base anything you want even negative numbers or imaginary numbers.

if you make the base to be (2i) every number real or complex can be represented only using the numbers 0-4 without the need for negative signs or i's .
Try it!

2323 in quarter imaginary system would be

2*(2i)^3+3*(2i)^2+2*(2i)+3= -2*8i+3*4+4i+3= 15-12i

or qigits. The drawback is that odd imaginary components require 'decimal' or quarterimaginarinal 'digits'

(0.2)= 2*(2i)^-1=-i so (10.2) = i

proving there is only one exact way to represent each number (except for infinite repeating decimals of highest value number like 0.9999999999999...=1 is much harder)

but Donald Knuth came up with this when he was only in middle school.

so to restate the begining joke but this time in the quarter imaginary system

There are 10.2 kinds of people I admire, those with the power to imagine

Donald Knuth