Hi Robin and welcome to Coin Talk! Here is a web site that explains what currency collectors call "Fancy Serial Numbers"! The serial number on your note is called a binary because it only has 2 numbers in the serial number! https://www.mycurrencycollection.com/reference/collecting/types-and-values-of-fancy-serial-numbers
I would keep it. Afterall, it only costs you a dollar to keep. I have bills that are binary numbers like this. Kinda difficult to come across. Someone on ebay would pay more than face value for it too probably.
Buyers of cool and fancy serial numbers also look at the condition of the note. Yours has circulation stains, folds and some kind of smear on the right serial number.
I'll take a shot at your question, even though I'm not a collector of serial numbers. Collectors always want to collect something that's rare, or that few other people have. With banknotes, that rarity can come from many things. It could be the number of notes initially printed, the number currently still in existence, a particular date or signature, a note in really super condition, an error made on very few notes, or a serial number that while not "rare" in the same sense as these other things, is "fancy" enough to make the note stand out from the rest. Not all collectors will stress all of the above in their collections, based their our own priorities and financial wherewithal. For example I don't collect serial numbers, but if you offered me one of two identically perfect notes with the same date and signatures at the same price, and one was serial 593745659 and one was serial 00000001, you bet I would want the second one.
Welcome to Paper Money forum of "Coin Talk" @Robin - @Dave M sums it up perfectly & then adds his own perspective since he's not a collector of special serial numbers. When I started to attend the odd coin show only a few dealers offered banknotes for sale in the GTA region (southern Ontario, Canada) 20 years ago. I heard a few collectors say that note had a fancy # in a mocking tone (like it was "close but no cigar") & then heard the term again online several years later. At that time it meant a number special only to a few collectors. The reason was very few people collected birthday notes, area code & other 'binary' (etc) fancy serial #. On the other hand, Special Serial numbers were becoming very popular & the catalogues had a section for these. Low serials (under 1000), radars, ladders & million # notes were about it. I like your note's 2 digit serial number but I wouldn't call it a binary (binaries are 1 & 0) nor call it 'special' so it wouldn't be on my radar. Some might call it 'fancy' & be tempted to collect (or acquire) it though. As @paddyman98 notes, the whole note is considered & the condition is sort of like location for real estate (pretty paramount) to most. But its a pretty cool find & I know I would be keeping it ($1) if it were me.
As pointed out above, a true binary is just 1s and 0s, like the computer code, but more importantly, condition is just about everything, as pointed out previously. The only notes in really poor condition that bring a premium are the really rare ones. Mismatched serial numbers would be one. Notes with multiple errors would also rank a premium. There are others, but so far out of the normal persons price range that we can only wish.
