79. Complete the Synchronous Down Counter for Launch Systems

Synchronous Down Counter: A sequential storage network where all constituent flip-flops are tied to a mutual clock, causing memory elements to recalculate and decrement simultaneously to eliminate propagation skew.

Rocket System Reset Functionality: Executing an active pulse via RST overrides normal clock states asynchronously, presetting Q3 and Q1 to 1 and clearing Q2 and Q0 to instantly lock the network at 1010.

1 Hz Time base Execution: The clock line ticks at a fixed interval of one pulse per second, stepping the logic safely and uniformly through each critical secondary milestone sequence.

Terminal State Interlocking: A combinational NOR block continuously watches the outputs; when 0000 is achieved, it pulls the steering lines low, turning off J and K across all stages to halt subsequent state variations.

• Combinational Steering Logic Synthesis: The countdown sequence, invalid-state recovery paths, and terminal lock condition were translated into a complete JK excitation table. Karnaugh-map minimization of the excitation functions yielded the following control equations:

  • J3 = 0

  • K3 = Q3·Q2'·Q1'·Q0'

  • J2 = Q3·Q1'·Q0'

  • K2 = Q3 + Q2·Q1'·Q0'

  • J1 = Q2·Q3 + Q2·Q0' + Q3·Q0'

  • K1 = Q1·Q0'

  • J0 = Q1·Q2' + Q2·Q3' + Q3·Q2'

  • K0 = 1

  • OF = Q3'·Q2'·Q1'·Q0'

• These equations generate the required steering signals for the JK flip-flops, ensuring correct countdown operation, recovery from invalid states, and overflow indication at the terminal state.

Overflow Notification: Simultaneous with the zero-state lock, the decoding gates force OF high (1), routing an official ignition authorization flag directly to the rocket's propulsion subsystem.