Hello fairyJo, thanks for your suggestions. I don't think I can wear a binary watch - I can actually tell the time in binary and I don't want everyone to know!
I don't mind what gender the watches are intended for and would happily wear a mans one, but it has to be approximately on the right scale for me to wear all the time - to work, in the kitchen, asleep, and everything - and I haven't seen anything suitable yet. I'll let you know what I find though! If you come across any other ideas, let me know.