Binary Numerals
October 13, 2015 · draft
One of my many fascinations, the study of counting systems has led to me embrace a passion for base-4. A few key points make this system more enticing than others. Besides being exceptionally easy to learn, it is delightfully easy to combine into pairs and triplets to become proficient in hexadecimal and base-64 as well. To facilitate … I have developed a new numeral system – a way of writing these numbers – that I would like to share. Unfortunately, save the time to actually try to draw these figures with graphics tool, I will have to present them in a ASCII art form. Many of these symbols are close enough to a common character equivalent that the entire system could almost be represented solely with LATIN characters. Unfrotunately a few of the characters are not so fortunate.
Base 4
We start with base-4 itself. The representation is quite simple. Zero is represented with an X, one is represented with a character resembling a C, two is simply the reverse – a backwards C, and finally three is similar to an O.
. . .---. .---. .---.
\ / | | | |
/ \ | | | |
' ' '---' '---' '---'
It is is not already obvious by looking at the symbols, the trick is that the side walls of the figures represent the binary places. Since X has no sidewalls it is zero; one has only the left sidewall; two the right sidewall; and, of course, O has both.
Base 16
Now let us turn to base-16, or hexadecimal.
. . . .---. .---.
\ / \ | | |
X '--\ | | |
/ \ | | | |
' ' '---' '---' '---'
. . .---. .---. .---.
\ / | | | |
X | | | |
/ \ | | | |
' ' '---' '---' '---'
. . .---. .---. .---.
\ / | | | |
X | | | |
/ \ | | | |
' ' '---' '---' '---'
. . .---. .---. .---.
\ / | | | |
X | | | |
/ \ | | | |
' ' '---' '---' '---'