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The Birkana hexadecimal number symbols
- xupybd 10y agoThat's just binary? I find hex notation much easier to use and to communicate verbally.
- ChuckMcM 10y agoI was thinking the same thing. If you're going binary just have a 4 x 4 dice face with different numbers of dots filled in.
- js8 10y agoFor fun, I have designed a font like that once. Each hex digit was 4x4 grid, and there were (visually distinct and symmetric if possible) patterns of 0-15 filled dots. I also thought about an extension for having a symbol for each byte value in 16x16 grid. The lower half byte would determine a 4x4 pattern, which would be repeated over the 16x16 grid according to the pattern corresponding to the higher half byte.
- colejohnson66 10y agoIf you can fit up to 16 "symbols" per "place", like you can here, it's hexadecimal, no? Either way, 0-F is a lot easier.
- FoeNyx 10y ago> Either way, 0-F is a lot easier. Easier for us because it's the conventional way hexadecimal was represented in computer history, and how we learned it. That rune-like system is more "logical" in the way you can visually read the value by summing the segments/bits value composing the berkanam rune from least significant at top to the most significant at bottom.
- nabla9 10y agoThere are 16 symbols, so it's hexadecimal. The symbols themselves neatly match the binary representation of 4 bits, so you can look at the numbers and see them as binary numbers in groups of four if you wish. These would be great hexadecimal symbols for programmers.
- Gracana 10y agoI get what the parent is saying, though. It's just binary digits on a weird looking vertical number line. Each part of the "digit" may as well be a zero or a 1, because that's all it represents. Position tells us what the value is, 2^0, 2^1, 2^2, or 2^3, no need for different symbols. And while we're at it, let's write it left-to-right MSB first, because that's how other numbers work, and it fits on a line nicely, like so: 0101.
- adrianratnapala 10y agoThe point is that as you get used to reading them, you will recognise the complete glyph as a hex digit, without puzzling over the binary details. Just like reading any other script. This does not work for quartets like 0100
- xupybd 10y agoThis is a good point, but you get the same from standard Hex notation. But standard Hex notation has the advantage that I can say FF to someone, but how do I pronounce these things? I guess this could have merit, but I just don't have much of an issue using standard Hex notation.
- zenobit256 10y agoHuh, you could use a double-sided version of this for a byte.
- jl6 10y agoI like it! Comes with a built-in eternal holy war over whether 0x16 goes top left or bottom left.
- hnsummarizer 10y agoTldr: "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.,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.,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.,I find it easiest to sum up starting at the highest possible number, then adding on the next-highest number, and so on. As you can see, every combination of the zero line and the accents will give us a hexadecimal number .,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.,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."
- andars 10y agoIs this a bot? This summary is nearly the length of the article, just lacking the actual images of Birkana symbols.
- grzm 10y agoI believe so, looking at the other comments it's posted in the hour it's been on the site: https://news.ycombinator.com/threads?id=hnsummarizer https://news.ycombinator.com/threads?id=hnsummarizer
- hnsummarizer 10y agoHello! I'm a human with a bot friend-- I read up on the debates about HN summaries and so I'll be making a chrome extension so that I don't provide previews to anyone that doesn't want one.
- szc 10y agoI think there is a problem with this notation - it is not self aligning. Meaning that if you hand wrote these you could then easily mis-read the values. It would probably be okay in printed form or if you were using lined paper, using the ruled line as a centre point.
- OMGWTF 10y agoCan you provide an example that could be misread? I think its quite easy to judge whether a downwards accent starts at the top of the line or at the middle, similarly for the upwards accent if it starts at the middle or at the bottom.
- szc 10y agoI may have made a mistake in assuming that the vertical line, because it was drawn in a different weight, was not part of the symbol. Without the line 1 & 4, 2 & 8 and 3 & 12 would rely on the vertical relationship with other symbols.
- smaddox 10y agoHow would you misread the values? I suppose the symbols for 0x1/0x4 or 0x2/0x8 could be written sloppily enough to be confused, but it's no worse than trying to distinguish sloppily-written arabic numeral symbols. In fact, I suspect that these would be significantly easier to distinguish.
- alias_ 10y agoI think it would be relatively hard to misread. If you really wanted to make it clear the top and botom lines could be drawn horizontally.
- FoeNyx 10y agoIt could also interestingly be mixed with reflected binary code [1] with only one segment changing between two successive values. > 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. There are already some runes encoded in unicode, but most of the symbols of the birkana system does not match any existing historical runes though. Yet, there is something in unicode that is somehow visually close [2]: braille patterns (2 columns of 4 rows of dots). But sadly the braille dots are not ordered in the same way because it was extended from 6 bits (from top to bottom : left column 123, right column 456) to 8 bits (from top to bottom : left column 1237, right column 4568). -- [1] https://en.wikipedia.org/wiki/Gray_code https://en.wikipedia.org/wiki/Gray_code [2] https://en.wikipedia.org/wiki/Braille_Patterns https://en.wikipedia.org/wiki/Braille_Patterns
- todd-davies 10y ago> 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. Could somebody explain how hexadecimal is more closely related to binary than any other base is? My only conclusion is that one hexadecimal digit is equivalent four binary digits.
- nine_k 10y agoOctal is 3 bits per digit, hexadecimal is 4. Either was / is widely used wherever you need to interact with bits (eg embedded development). But 10-based cannot be easily mapped to binary, so does not work as well.
- andars 10y agoI would say your conclusion is right. Some bases don't really make sense to use in conjunction with binary (5, 7, 10, etc.) but any power of two "works". I prefer hex to octal because a byte splits nicely into two hex digits.
- deleted 10y ago[deleted]
- maaaats 10y agoBases in 2^n can be easily converted between, as you can consider each group/symbol independently when converting.
- lucb1e 10y agoWhat I find the neatest is that it's not just showing hexadecimals, but the binary representation at the same time. In the Birkana symbol for 9 it's very easy to recognize the binary 1001: it has the top and bottom 'bits' set. It also made me aware that I never thought about the symbols we use for numbers. Our digits 0 through 9 suddenly seem very arbitrary, looking at Birkana. Though ten digits are more difficult than sixteen to represent this way, they could certainly have had logic in them.
- yawaramin 10y agoAs for the logic behind our decimal digits, there was an explanation going around for it, but at best it's probably reaching very hard. I'll let you decide: http://message.snopes.com/showthread.php?t=49183 http://message.snopes.com/showthread.php?t=49183
- drostie 10y agoThe actual logic is a bit more benign. Once upon a time, the digit for 0 was a dot, the digit for 1 was (close to) ι, the digit for 2 was (close to) μ, the digit for 3 was close to w with a leading descender like μ has. The digit for 4 might have been closer to a + sign that eventually morphed to look more like a backwards 2. It was the number of vertical lines which encoded 1, 2, or 3; with 4 and 5 and 6 there was more need to come up with more-abstract symbols. In Arabic these first 4 digits have actually survived relatively unmolested, ٠ - ١ - ٢ - ٣, while the backwards 2 for 4 started hooking down to become a ٤ and some other stuff happened with the next 5 digits. In English the digits for 2, 3, and 4 all rotated about 90 degrees counterclockwise while the tail disappeared for the 3 and the 4 didn't close up on the top until relatively late.
- david-given 10y agoFun fact: you can count to hexadecimal on the fingers of one hand. The way it works is that each of your four fingers has four well-defined places on them: the three joints, plus the tip. You use your thumb to point at one of these. The first finger represents 1-4, the second 5-8, the third 9-12, the fourth 13-16. You count up and down by moving your thumb. Also, because you use the thumb of the same hand for pointing, you can count two different hexadecimal numbers if you use both hands --- which means you can count to 256. (I don't know anybody limber enough to do this with their toes.) As a special bonus: if you point to the fleshy pads of the fingers instead of the joints, you can use the same system for base 12.
- daeken 10y agoCounting in binary gets you even further. If each finger is one bit, you can easily count to 2^10-1 == 1023. I frequently use this to keep track of running totals over 10.
- kmill 10y agoIn my high school orchestra, I'd count the rest measures on my cello's fingerboard using binary. Usually I'd only need four fingers, but occasionally I'd need my thumb as well if the composer mistook the cello for a bass.
- khedoros1 10y agoThere was a teacher in high school that taught his classes to count in binary on their fingers. It became common for students to flip the double bird at each other in the halls yelling "132!"
- lern_too_spel 10y agoThis method is impractical to use due to the way the human hand works. Representing numbers where the middle and ring fingers are in different positions is tricky, and using this method for counting quickly is nearly impossible because it requires the simultaneous movement of multiple fingers up and down. The method of counting on finger creases, on the other hand, is entirely practical, and I've known people who have used it for more than 50 years.
- pygy_ 10y agoThe bibi-binary notation is somewhat similar (16 === 2^2^2). It was patented in 1968 by Bobby Lapointe, a French variety singer, but didn't get much traction AFAICT. Bibi-binary also has a custom pronunciation for hex digits. The article is in French[0], but the main illustration that describes the system is self-explanatory[1]. 0. https://fr.wikipedia.org/wiki/Syst%C3%A8me_Bibi-binaire https://fr.wikipedia.org/wiki/Syst%C3%A8me_Bibi-binaire 1. https://upload.wikimedia.org/wikipedia/commons/a/a0/Table_de_correspondance_entre_le_Bibinaire_et_les_autres_notations.svg https://upload.wikimedia.org/wikipedia/commons/a/a0/Table_de...
- zokier 10y agoWhat's with the different BI/KI shapes? I would have expected them to be just rotated variations of each other, like for example BA/KE are
- blahedo 10y agoThe shapes are all able to be written in a way that visits points in the corners of the square in the same order (UL, LL, UR, LR). So 0111 and 1110 can be written with the skewed V shape because the 1's are in sequence, while 1011 and 1101 are written with rotated L shapes because they skip one of the middle bits. (Compare also 1111, a backwards N shape).
- blahedo 10y agoI just translated the article to English; see https://en.wikipedia.org/wiki/Bibi-binary https://en.wikipedia.org/wiki/Bibi-binary .
- lccarrasco 10y agoThanks a lot! :)
- sharkjacobs 10y agoit would be nice, just generally, not to introduce another character which is just a plain vertical line, even if 99.9% of the time it is identifiable by context
- fatihpense 10y agoI had reinvented these symbols, without knowing Birkana, for one of my hobby alphabets at high school. I had given a lot of thought with my high-schooler leisure time and haven't been able find more simple system with enough data capacity. I think readability suffers from similarity though. They also look like some symbols from Old Turkic alphabet, If I recall correctly it was my source of inspiration: https://en.wikipedia.org/wiki/Old_Turkic_alphabet https://en.wikipedia.org/wiki/Old_Turkic_alphabet
- ajb 10y agoThe geomantic figures (https://en.wikipedia.org/wiki/Geomantic_figures https://en.wikipedia.org/wiki/Geomantic_figures) can also represent 4 bit values. Unfortunately they aren't in unicode either. The Ba gua (https://en.wikipedia.org/wiki/Bagua https://en.wikipedia.org/wiki/Bagua) are, but can only represent 3 bits per symbol.
- porges 10y agoThe Tài Xuán Jīng symbols are, however. A subset can be used like: 𝌆𝌇𝌉𝌊𝌏𝌐𝌒𝌓𝌡𝌢𝌤𝌥𝌪𝌫𝌭𝌮 So Unicode has Bagua (3 bits), Tài Xuán Jīng (4 trits), and I Ching (6 bits, but incomplete).
- userbinator 10y agoIt somewhat reminds me of this: https://en.wikipedia.org/wiki/File:Bruce_Martin_hexadecimal_notation_proposal.png https://en.wikipedia.org/wiki/File:Bruce_Martin_hexadecimal_... I've also seen various notation for writing numbers in hex used by some reversers/crackers/demosceners mostly from Eastern European countries, who probably used hex enough to develop something similar to a stylised form of 0-F but distinctly different from those letters/numbers for easier reading and writing. (This was when home computers were still relatively new, and it was usual to make great amounts of handwritten material when working with them.)
- igaray 10y agoI like the 12480 script http://www.omniglot.com/conscripts/12480.htm http://www.omniglot.com/conscripts/12480.htm
- deleted 10y ago[deleted]