This website blog chronicles my exploration into using symbology to represent alternative numerical base systems. My ultimate goal is to uncover and simplify known, and unknown, mathematical processes and connections between these systems. This is a hobby and should be taken as such. Thanks for visiting.

019 Binquadratetric (65536) Introduction

A 16-bit number can distinguish 65536 different possibilities, such as the numbers 0..65535.


Base 65,536? Am I crazy? Maybe. This base glyph system toggles on and off 16 segments to create 65,636 different combinations. It is really just a compact form of displaying 16 binary digits.

Unfortunately, it does not contain many factors, especially when you consider it’s size: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536.


Each glyph contains four quadrants. It’s easier to differentiate the glyphs by breaking them down into their individual quadrants. Each quadrant can be thought of as a sub-digit of binquadric (hexadecimal).


Each sub-digit of binquadric toggles on and off four segments to create sixteen different combinations. The chart above shows the numerical value of each Binquadric sub-digit. Similar to Binquadric numerals, a specific segment is used to represent each binary sub-digit:

1 = Vertical Line
2 = Back Slash
4 = Horizontal Line
8 = Slash

By using different combinations of these four segments, all sixteen combinations can be represented.

These Binquadric sub-digits start at the lower right quadrant and wrap up and around to the other side. The pattern is continued to the next glyph. This creates a snake like
sinusoidal pattern of reading which cuts down on unnecessary eye movement.


This example above shows a four digit Binquadratetric number and its sixteen sub-digits of Binquadric. If we rearrange the quadrants into a strait line, we can see the string of Binquadric sub-digits a little better.




tbq3a tbq3b tbq3c

Here are some animated examples of three digit numbers in Binquadratetric. A three digit binquadratetric number can range anywhere from zero to 281,474,976,710,656. (281,474,976,710,656 equals two to the power of forty eight)