Memorising binary digits has, again, been part of memory competitions almost since the start, although only as a 30-minute discipline until 2006. It's also always been the rule that they are presented in rows of 30, unlike decimal digits which come in rows of 40, and there's a simple reason for that - everyone always used to memorise them by turning each group of three binary digits into a single decimal number from 0 to 7, and memorising that. It was just another decimal digits task, with an extra step included.
Dominic, apparently not being familiar with how binary numbers work, changed them into decimal numbers in a different way that made sense to him, but still just converted groups of three into a number from 0 to 7. Andi had an anecdote about how he once got half way through recalling before he realised he was writing down decimal numbers instead of ones and zeros. Neither of them were big fans of the whole idea of binary digits in memory competitions.
I think I can take the credit for being the first to do something different, and even then my system is still only subtly changed from that basic principle - even so, binary is something where there's always been a big gap between the best and the rest. And scores have leapt up since people first started doing it; the current world record for 5-minute binary would have comfortably won the first 30-minute binary event, back in 1993.
When I first started out, I wasn't a fan of binary either - I created a really rubbish category-based person-action-person system and persevered with it for much too long, before coming up with an idea that worked. But when I did, binary quickly transmogrified into a great favourite! And I think there's always something cool about being able to say you remember three or four thousand digits of ones and zeros - it's probably the score that sounds the most mind-boggling to the uninitiated!