
A BISENARY NUMBER SYSTEM
How Do You Count?
Our counting system is set in base10, also known as decimal (Greek: deca), because we use 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent the integers. If we have only 0 and 1, the number system will be binary (Latin: bi), and we count like this:
0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, …
Another system related to computing is base16 (Greek: hexadecimal), where the digits are 0 to 9, followed by A, B, C, D, E, and F. For example, just as the number 5827 in decimal actually represents the sum of 5 thousands (10^{3}), 8 hundreds (10^{2}), 2 tens (10^{1}), and 7 ones (10^{0}), so the hexadecimal number E2A9 represents the quantity 58025 (when written in decimal) as the following sum.
E2A9 = 14 × (16^{3}) + 2 × (16^{2}) + 10 × (16^{1}) + 9 × (16^{0}) = 58025
Why 36?
Now if we extend this 16digit idea by exhausting the entire English alphabet (26 letters from A to Z), then we get a system of counting in base36 (0 to 9 plus A to Z).
We do not know if base36 has a name, but we know that a base6 counting system (employing only the digits 0 to 5) is called senary (Latin: sex). Since 36 = 6^{2}, we can view base36 as a senary with digital grouping of two, i.e., with a separating comma every other digit, e.g., we write the senary number 3550124 as 03,55,01,24. In all we are dealing with 36 possible pairs of digits (each digit being 0, 1, 2, 3, 4, or 5), ranging in decimal values from 0 to 35:
00, 01, 02, 03, 04, 05, 10, 11, 12, 13, 14, 15, 20, … , 54, 55
We then simplify: 00 = 0, 01 = 1, … , 54 = Y, 55 = Z, and omit the commas, e.g., 3550124 (base6) is now written 3Z1G (base36).
Thus the name bisenary, our own definition.
What Is Your Number?
Hence every word can be treated as a bisenary number or be converted to a decimal value. For instance, we find that the name Bob is equivalent to 15131:
BOB = (11 × 36^{2}) + (24 × 36) + (11 × 1) = 15131
Your required contribution is to write a program to do the conversion between decimal and bisenary. Choose a programming language of your preference, making sure that from bisenary to decimal the user may input a lowercase digit (a) instead of uppercase (A).
To do the converse, from decimal to bisenary, you will deal with further mathematical reasoning. As a crude sample, this part has been implemented in JavaScript at the top of this page. Feel free to save a copy or modify this file as needed.
Copyright © 2013–2018 Amin Witno
This page belongs to the personal folder of Amin Witno and does not necessarily represent the philosophy and values of Philadelphia University or the Department of Basic Sciences in particular.

