The maximum clock frequency for a synchronous sequential circuit is limited by the timing parameters of its flip-flops and gates. These parameters include propagation delays, setup times, and hold times. The minimum clock period is the reciprocal of the maximum clock frequency. For a specific 7474 circuit, the maximum clock period must be greater than or equal to 60 ns to account for the propagation delays and setup time of the flip-flops.

1. Maximum Clock Frequency The clock frequency for a synchronous sequential circuit is limited by the timing parameters of its flip-flops and gates. This limit is called the maximum clock frequency for the circuit. The minimum clock period is the reciprocal of this frequency. Relevant timing parameters Gates: Propagation delays: min t PLH , min t PHL , max t PLH , max t PHL Flip-Flops: Propagation delays: min t PLH , min t PHL , max t PLH , max t PHL Setup time: t su Hold time: t h

2. Example T W ≥ max t PFF + t su For the 7474, max t PLH = 25ns, max t PHL = 40ns, t su = 20ns T W ≥ max (max t PLH + t su, max t PHL + t su) T W ≥ max (25+20, 40+20) = 60

3. Example T W ≥ max t PFF + max t PINV + t su

4. Example T W ≥ max t PFF + max t PMUX + t su

5. Example Paths from Q1 to Q1: Paths from Q1 to Q2: Paths from Q2 to Q1: Paths from Q2 to Q2: None T W ≥ max t PDFF +t JKsu = 20 +10 = 30 ns T W ≥ max t PDFF + max t AND + t JKsu = 20 + 12 + 10 = 42 ns T W ≥ max t PJKFF + t OR + T Dsu = 25 + 10 + 5 = 40 ns T W ≥ max t PJKFF + max t AND + t JKsu = 25 + 12 + 10 = 47 ns TW ≥ 47 ns

6. Example T W ≥ max t PFF + max t PINV + t su

7. Example T W ≥ max t PFF + max t PMUX + t su

8. Example Paths from Q1 to Q1: Paths from Q1 to Q2: Paths from Q2 to Q1: Paths from Q2 to Q2: None T W ≥ max t PDFF +t JKsu = 20 +10 = 30 ns T W ≥ max t PDFF + max t AND + t JKsu = 20 + 12 + 10 = 42 ns T W ≥ max t PJKFF + t OR + T Dsu = 25 + 10 + 5 = 40 ns T W ≥ max t PJKFF + max t AND + t JKsu = 25 + 12 + 10 = 47 ns TW ≥ 47 ns