Based on the following circuits, find values read at state Q at the time i Q & R S Time i S 1 R 0 Qn+1 0 1 0 0 2 0 1 3 0 0 4 1 0 0 0 6 0 1 7 0 0 8 1 0 9 0 10

Database System Concepts
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Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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### SR Latch Circuit Analysis

**Circuit Diagram:**

The diagram showcases an SR latch made from NOR gates. The latch includes:
- Two inputs labeled as R (Reset) and S (Set).
- Two outputs, Q and \(\overline{Q}\). \(\overline{Q}\) is the complement of Q.

The circuit is a cross-coupled configuration where the output of one NOR gate is connected to the input of the other.

**Truth Table:**

Below is the truth table for the SR Latch. The table represents how the values change over time \(i\) based on inputs S and R:

| Time \(i\) | S   | R   | \(Q_{n+1}\) |
|------------|-----|-----|-------------|
| 0          | 1   | 0   |             |
| 1          | 0   | 0   |             |
| 2          | 0   | 1   |             |
| 3          | 0   | 0   |             |
| 4          | 1   | 0   |             |
| 5          | 0   | 0   |             |
| 6          | 0   | 0   |             |
| 7          | 0   | 1   |             |
| 8          | 1   | 0   |             |
| 9          | 0   | 0   |             |

**Explanation:**

- **Input S (Set):** When S = 1 and R = 0, the latch sets Q to 1.
- **Input R (Reset):** When R = 1 and S = 0, the latch resets Q to 0.
- **Hold State:** When S = 0 and R = 0, Q holds its previous state.
- Undefined behavior occurs when both S and R are 1.

Use this configuration as a basic building block in sequential logic circuits. Instructions may involve filling out the future states for each time \(i\) based on initial conditions and subsequent input variations.
Transcribed Image Text:### SR Latch Circuit Analysis **Circuit Diagram:** The diagram showcases an SR latch made from NOR gates. The latch includes: - Two inputs labeled as R (Reset) and S (Set). - Two outputs, Q and \(\overline{Q}\). \(\overline{Q}\) is the complement of Q. The circuit is a cross-coupled configuration where the output of one NOR gate is connected to the input of the other. **Truth Table:** Below is the truth table for the SR Latch. The table represents how the values change over time \(i\) based on inputs S and R: | Time \(i\) | S | R | \(Q_{n+1}\) | |------------|-----|-----|-------------| | 0 | 1 | 0 | | | 1 | 0 | 0 | | | 2 | 0 | 1 | | | 3 | 0 | 0 | | | 4 | 1 | 0 | | | 5 | 0 | 0 | | | 6 | 0 | 0 | | | 7 | 0 | 1 | | | 8 | 1 | 0 | | | 9 | 0 | 0 | | **Explanation:** - **Input S (Set):** When S = 1 and R = 0, the latch sets Q to 1. - **Input R (Reset):** When R = 1 and S = 0, the latch resets Q to 0. - **Hold State:** When S = 0 and R = 0, Q holds its previous state. - Undefined behavior occurs when both S and R are 1. Use this configuration as a basic building block in sequential logic circuits. Instructions may involve filling out the future states for each time \(i\) based on initial conditions and subsequent input variations.
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