For the last couple months a friend and I have been working on a 4000 series based clock in electronics class. After having failed building a FM receiver, we opted for a clock. We didn't go the microcontroller way, but old school ICs. So, we created a circuit for a simple clock. I opted for a 24-hour version, while my friend made the 12-hour equivalent.
The above image was the basis of the circuit. Not shown was a 4060 and 4013 IC to make a nice 1Hz signal which we can use for the seconds. The rest is fairly simple: allow the seconds and minutes to count to 59 and use AND gates to reset at 60. Also pictured is the buttons to set the time. We used two 2N2222 transitors to make a NOT gate. Though, this ended up being too glitchy so I opted for a 4011 to create stable square wave.