I've been contemplating about using TTL logic or an Arduino. I mean, if I were to use a crystal and divide it down to a 1 hertz signal, will it seriously be THAT inaccurate to be worth caring about? Like if it's a few seconds a year, then I could care less. Also, I've never used an arduino, and this project, should I go with an arduino, would be my first project with it, whereas with the TTL logic, I already have a pretty good idea of how to make my clock with TTL logic, with a few 4017 IC's and some clever use of logic gates.
Opinions?
Arduinos typically suck for timing accuracy because they use a ceramic resonator rather than a crystal however some Arduino clones use a real crystal for the main MCU. With careful calibration, you can keep time on an Arduino to a few seconds per day, but if you want to do any better you need either a RTC or a high accuracy low frequency external clock pulse. Also, unless significantly modified, it isn't easy to provide battery backup to most Arduinos as they aren't optimised for low power consumption. This means that an Arduino based clock is typically over-complex compared to one built around a 'bare' ATmega328P.
Crystals really aren't that good for timekeeping. A typical MCU crystal has a tolerance of +/-30 PPM, which is about 15 minutes per year. Careful trimming and close temperature control can improve that by about one order of magnitude, but if you want to do better than that you need to sync with one or more atomic clocks - and its most cost effective to let someone else fund and maintain them, hence the popularity of GPS receivers for timekeeping or NTP over the internet. There are also various broadcast timesignals on the LW or MW bands but there's also a lot of interference on those bands and unless you have a background in Ham DX receiver construction or are near enough to a well funded timesignal station to get a very strong signal, its a PITA.
It's really awkward to build an accurate 'retro' clock in pure logic with no MCUs, FPGAs or other 'cheats', as to get anything better than crystal accuracy rapidly gets expensive, both to build and to run. Probably the cheapest option is to divide down the output of a Rubidium oscillator module off EBAY . . . .