## Oct 16, 2016

### The Birkana hexadecimal number symbols

AMONG number systems, the hexadecimal system of counting (or 'radix') has a special place in the hearts of programmers, being closely related to binary, the fundamental number system used by all modern computers. Unlike decimal, which counts ten numbers (0 through 9) before having to add a 'place' (an order of magnitude), hexadecimal allows us to count sixteen numbers (0 through 9, then A through F) before having to add a place.

While the hexadecimal notation of using the first six letters of the alphabet is practical in a rough-and-ready sort of way, no one ever accused it of being elegant. There does, however, exist a fairly elegant (and I think clever) notation for writing hexadecimal--it's called Birkana. The only problem with Birkana is that most of the internet seems to have forgotten about it.

Well, almost all. I obviously came across Birkana somewhere on the internet at some point, years ago. And there may well be many posts written about it in the back reaches of the Google search engine. But to this day, the only result I've managed to find in my searches has been a mailing list post in the discussions of The International Slide Rule Group--probably not a very prominent corner of the online world.

That's too bad, because Birkana is pretty cool and it does deserve a proper introduction. So, what is it exactly?

Birkana is a Runic symbol set for expressing the hexadecimal number radix, but it's designed in such a way that the exact shape of each number rune is built by combining a basic shape for the number zero and accents which correspond to the numbers 1, 2, 4, and 8. In the right combinations, they can express any number from 0 to F. Here are the shapes for the 'building block' numbers:

0x0

0x1

0x2

0x4

0x8

As you can see, every combination of the zero line and the accents will give us a hexadecimal number (between 0 and F). I find it easiest to sum up starting at the highest possible number, then adding on the next-highest number, and so on. Some examples:

0x3 (= 0x2 + 0x1)

0x6 (= 0x4 + 0x2)

0x9 (= 0x8 + 0x1)

0xD (= 0x8 + 0x4 + 0x1)

0xF (= 0x8 + 0x4 + 0x2 + 0x1)

Notice also the exact positions of the accents--they intersect with the zero line at either the top, middle, or bottom, and they end up parallel to exactly a quarter of the way up or down the zero line. The design may have been inspired by ancient runes, but it is very carefully thought-out.

Unfortunately, at the moment it's not practical to type in Birkana in any digital format. Theoretically, the Unicode Consortium could decide to add the Birkana symbols to the Unicode specification and some enterprising font designer could come up with a set for general use. Until then, you're unlikely to come across Birkana symbols on the internet. So for now, enjoy them here, and feel free to copy the SVG shapes off this page's source.