Use of decoders and comparators. Confirmation of expertise generating functions with multiplexers. Overview This circuit has many applications including detonators, alarm clocks, egg-timers and so on.
Details Work in pairs.
The cascade of the two circuits takes a little thought. The clock to the modulo-6 counter will be derived by your own circuitry and will have no direct connection to the 555. What you will have constructed is a 60 second count-down timer. Use comparators to detect the state 00, and freeze the counter. For your most complicated Boolean functions, use multiplexers.