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I've posted this everywhere else, might as well put it here as well. I was struck with the urge to see what digits and displayed on a 7-segment LED would look like applied to each other with binary logical operators. No particular reason other than being on an exercise bike a lot and staring at the display, doing my normal focus before/focus behind eye tricks with the digits. It made me curious what the results would look like, and would any of them result in a completely unique new set of characters. Not immediately impossible, since there are 2^7=128 possible characters to work with. Could you use this to represent an arithmetical operator?
NOR: Super sparse. Not very interesting.
OR: The inverse of NOR, thus super dense. Mostly 8s and 9s which isn't very interesting.
AND: Lots of recognizable characters. Which is bad for my purposes, but cool to see the patterns. I'd never thought before how digit shapes generally get more dense as they get larger. (With the notable exception of 7.)
NAND: More fun alien characters than AND, at least. Starting to feel like a cheap effect from an 80s SF film. (That's not a bad thing!)
XNOR: The rarest and most mysterious of all the commutative binary logical operators! The result of anything with 8 is itself, which is cool but not very useful.
XOR: My longtime favorite operator, and it doesn't let me down here. The output isn't quite unique, sadly, see 5/8 and 6/9, among others, and all the identity results are blank. But it comes close!
The next step is to see if the standard Hindu-Arabic numeral representation can be changed to give a unique grid. Unfortunately, these plots make it clear that we're extremely constrained in what could possibly work. Most of the operators fail completely when it comes to the identity output, of a digit being applied to itself. Only NAND and NOR can give unique results there, so if this idea is going to work, it has to be one of them. Intuitively, NOR looks way too spare to make it work, but maybe that's erroneous. Both NAND and NOR give so many duplicates that it's obvious that the digit design change will have to be quite extreme to have a chance of making it work.
NOR: Super sparse. Not very interesting.
OR: The inverse of NOR, thus super dense. Mostly 8s and 9s which isn't very interesting.
AND: Lots of recognizable characters. Which is bad for my purposes, but cool to see the patterns. I'd never thought before how digit shapes generally get more dense as they get larger. (With the notable exception of 7.)
NAND: More fun alien characters than AND, at least. Starting to feel like a cheap effect from an 80s SF film. (That's not a bad thing!)
XNOR: The rarest and most mysterious of all the commutative binary logical operators! The result of anything with 8 is itself, which is cool but not very useful.
XOR: My longtime favorite operator, and it doesn't let me down here. The output isn't quite unique, sadly, see 5/8 and 6/9, among others, and all the identity results are blank. But it comes close!
The next step is to see if the standard Hindu-Arabic numeral representation can be changed to give a unique grid. Unfortunately, these plots make it clear that we're extremely constrained in what could possibly work. Most of the operators fail completely when it comes to the identity output, of a digit being applied to itself. Only NAND and NOR can give unique results there, so if this idea is going to work, it has to be one of them. Intuitively, NOR looks way too spare to make it work, but maybe that's erroneous. Both NAND and NOR give so many duplicates that it's obvious that the digit design change will have to be quite extreme to have a chance of making it work.
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