Answer:
Step-by-step explanation:
To design a state diagram, table, K-map, and equation for a parking lot with an up-down counter application, we need to follow these steps:
Define the problem and identify the inputs and outputs.
Create a state diagram to represent the behavior of the system.
Generate a state table based on the state diagram.
Simplify the state table using Karnaugh maps (K-maps).
Derive a minimized equation for the next state.
Implement the equation using D flip-flops.
Step 1: Define the problem and identify the inputs and outputs.
The problem is to design a parking lot with an up-down counter application. The input to the system is a signal that indicates whether a car has entered or exited the parking lot. The output is the current number of cars in the parking lot.
Step 2: Create a state diagram to represent the behavior of the system.
The state diagram for the parking lot with an up-down counter application is as follows:
lua
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+-----+ +-----+
| | | |
| | | |
V | | V
+------------+ | +------------+
| Car Enters | | | Car Exits |
+------------+ | +------------+
| | | |
| V V |
| Count Up/Down |
| |
+-----------------+
Step 3: Generate a state table based on the state diagram.
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+------------+------------+------------+------------+
| Current | Input | Next State | Output |
| State | | | |
+------------+------------+------------+------------+
| 00 | 0 | 00 | 00 |
| 00 | 1 | 01 | 01 |
| 01 | 0 | 01 | 01 |
| 01 | 1 | 10 | 02 |
| 10 | 0 | 10 | 02 |
| 10 | 1 | 11 | 03 |
| 11 | 0 | 11 | 03 |
| 11 | 1 | 10 | 02 |
+------------+------------+------------+------------+
Step 4: Simplify the state table using K-maps.
We can simplify the state table using K-maps as follows:
mathematica
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Input: 0 Input: 1
+-------+-------+ +-------+-------+
| | | | | |
| 00 | 01 | | 01 | 10 |
| | | | | |
+-------+-------+ +-------+-------+
Input: 0 Input: 1
+-------+-------+ +-------+-------+
| | | | | |
| 01 | 10 | | 11 | 10 |
| | | | | |
+-------+-------+ +-------+-------+
Input: 0 Input: 1
+-------+-------+ +-------+-------+
|