U-value Number System

This is a proposal for a number system to be used in the computation/storage of complex numbers, the term U-value comes from the Universal set, in this case it is C but the system uses a lowercase c in notation.

U-value Binary holds { n, i, c, r }, that is:
[Naught = 0, Imaginary = 1i, Complex = (1+1i), Real = 1]

Example 1: irc == 3+5i == 4i + 2 + (1+1i)
Example 2: cnir == 9+10i == (8+8i) + 0 + 2i + 1
Example 3: ccnn == 12+12i == (8+8i) + (4+4i) + 0 + 0

If the system is balanced (negative elements analog to i, c & r) it could be used to represent all Gaussian integers. The letters used have obvious reasons but to a computer it wouldn’t matter and could be re-worked to parrallel binary, for example U-value holds { 00, 01, 11, 10 } or whatever transmutation is best suited. With that set up the three examples look like this:

Example 1: irc == 00011011
Example 2: cnir == 11000110
Example 3: ccnn == 11110000

Although this does half the storage and if the system was balanced three nibbles would be needed (the extra place indicating negative or not 010 = 1, 110 = -1). With a set of rules for arithmatic, This could be useful for modeling fractals in a virtual computer or simulating situations, like in engineering, where imaginary and complex mathematics are key.


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