JK Flip-Flop: Hold Violation Risk from Toggle Operation
A synchronous circuit features a positive-edge-triggered JK flip-flop driving a downstream positive-edge-triggered D flip-flop. The JK flip-flop operates in conditional toggle mode: it toggles its output Q_JK on the LOW-to-HIGH transition of CLK when EN is 1, and holds its value when EN is 0. The propagation delay (t_pcq) of the JK flip-flop is 0.5 time units, while the D flip-flop requires a hold time (t_hold) of 1.0 time unit. Because t_pcq is strictly less than t_hold, any clock edge that causes Q_JK to change will violate the D flip-flop's hold window and drive its output Q_D into an indeterminate state.
Four signals are shown: CLK (clock, period 2), EN (toggle enable input), Q_JK (JK flip-flop output), and Q_D (downstream D flip-flop output).
Trace both Q_JK and Q_D across all 10 time steps.
Constraints
- Use
Xfor any time step where a hold violation occurs and for the duration that the indeterminate state persists. - The D flip-flop recovers from an
Xstate only if it successfully samples a stable, valid input at a subsequent clock edge. - Assume both
Q_JKandQ_Dare initially 0 at time step 0.
Topics
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