Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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**Q1. Timing Analysis (Graded for Completion)**

The diagram illustrates a digital circuit with various logic gates and flip-flops. The key components include:

- **Two-Input XOR Gates**: Each XOR gate in the circuit has a propagation delay of 80 picoseconds (ps) and a contamination delay of 40 ps.

- **Flip-Flops**: Each flip-flop includes a setup time of 80 ps, a hold time of 50 ps, a clock-to-Q propagation delay of 100 ps, and a clock-to-Q contamination delay of 70 ps.

**Question:**

(a) If there is no clock skew, what is the maximum operating frequency of the circuit?

---

**Explanation:**

The circuit diagram likely involves various interconnections between XOR gates and flip-flops, driven by a clock signal (CLK on the left and right sides of the circuit). 

To calculate the maximum operating frequency without clock skew, evaluate the critical path that determines the longest delay through the circuit. This delay dictates the shortest possible clock period, and hence the highest clock frequency that can be used reliably without data setup and hold timing violations in the flip-flops. 

Further analysis requires summing up delays from the components along the critical path, including XOR gate delays and flip-flop clock-to-Q delays, and then deriving the corresponding frequency.
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Transcribed Image Text:**Q1. Timing Analysis (Graded for Completion)** The diagram illustrates a digital circuit with various logic gates and flip-flops. The key components include: - **Two-Input XOR Gates**: Each XOR gate in the circuit has a propagation delay of 80 picoseconds (ps) and a contamination delay of 40 ps. - **Flip-Flops**: Each flip-flop includes a setup time of 80 ps, a hold time of 50 ps, a clock-to-Q propagation delay of 100 ps, and a clock-to-Q contamination delay of 70 ps. **Question:** (a) If there is no clock skew, what is the maximum operating frequency of the circuit? --- **Explanation:** The circuit diagram likely involves various interconnections between XOR gates and flip-flops, driven by a clock signal (CLK on the left and right sides of the circuit). To calculate the maximum operating frequency without clock skew, evaluate the critical path that determines the longest delay through the circuit. This delay dictates the shortest possible clock period, and hence the highest clock frequency that can be used reliably without data setup and hold timing violations in the flip-flops. Further analysis requires summing up delays from the components along the critical path, including XOR gate delays and flip-flop clock-to-Q delays, and then deriving the corresponding frequency.
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