3-Variable Boolean Expression Simplifier

A robust tool that simplifies 3-variable Boolean expressions using Karnaugh Map (K-map) logic. This project provides two separate implementations: one for the Arduino platform with a serial interface, and another for an 8051 (AT89S52) microcontroller with a keypad for input and an LCD for output.

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📚 Table of Contents

• About The Project
• Features
• Project Structure
• Implementations
  • 1. Arduino Version
  • 2. 8051 (AT89S52) Version
• How It Works
• License

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🎯 About The Project

This project was developed to provide a practical demonstration of digital logic simplification on embedded systems. It takes a set of minterms for a 3-variable (A, B, C) Boolean function and outputs the minimized Sum-of-Products (SOP) expression.

The core logic is based on the Karnaugh Map method, systematically identifying groups of 4 (quads), 2 (pairs), and 1 (singletons) to find the most simplified logical expression.

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✨ Features

• K-Map Logic: Implements the simplification algorithm by finding essential prime implicants.
• Dual Implementations:
  • Arduino: Easy-to-use interface via the Serial Monitor. Displays the full truth table, original SOP, and simplified SOP.
  • 8051: Standalone embedded system using a 4x3 keypad and a 16x2 LCD.
• Handles All Cases: Correctly simplifies any combination of minterms from 0 to 7, including the edge cases for functions that are always 0 or 1.
• Proteus Simulation: Includes a complete Proteus simulation file for the 8051 circuit, allowing for virtual testing without physical hardware.

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🚀 Implementations

This repository contains two versions of the project.

1. Arduino Version

This version is designed for quick testing and detailed output. It communicates with a computer via a USB connection and the Arduino IDE's Serial Monitor.

Hardware Requirements

• An Arduino board (e.g., Arduino Uno, Nano)
• USB Cable

Software Requirements

• Arduino IDE

How to Use

1. Open the Arduino_implementation/boolean_simplifier.c file in the Arduino IDE.
2. Select your board and port from the Tools menu.
3. Upload the sketch to your Arduino.
4. Open the Serial Monitor (Ctrl+Shift+M) and set the baud rate to 9600.
5. Enter the minterms you want to simplify, separated by spaces (e.g., 1 3 4 5 7), and press Enter.
6. The Arduino will print the truth table, the full SOP expression, and the final simplified expression.

2. 8051 (AT89S52) Version

This is a standalone hardware implementation that does not require a computer to operate once programmed. It's ideal for a dedicated lab tool.

Hardware Requirements

• AT89S52 Microcontroller
• 16x2 LCD Display
• 4x3 Matrix Keypad
• 11.0592 MHz Crystal Oscillator with two 33pF capacitors
• Power supply components (capacitors, resistors)

Software Requirements

• Keil µVision IDE (for compiling the C code)
• Proteus Design Suite (for running the simulation)
• An 8051 programmer (if building physical hardware)

How to Use (Proteus Simulation)

1. Open the 8051_simplifier/proteus_simulation/embedded.pdsprj file in Proteus.
2. Double-click the AT89S52 microcontroller component.
3. In the properties window, click the folder icon next to "Program File" and navigate to the 8051_simplifier/boolean_simplifier.hex file.
4. Click OK to load the hex file.
5. Run the simulation (▶️ button).
6. Use the virtual keypad to enter minterms (0-7).
7. Press the '#' key to calculate. The simplified expression will be displayed on the LCD.

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🧠 How It Works!

The simplification logic for both versions relies on the same core algorithm:

1. Minterm Masking: User inputs (e.g., 1 3 7) are converted into a single 8-bit integer (a bitmask). For the input 1 3 7, the mask would be 10001010 in binary (bits 1, 3, and 7 are set).
2. Hierarchical Grouping: The algorithm checks for groups in a specific order to ensure the largest possible groups are found first (as per K-map rules).
   • Quads (Groups of 4): It first scans for all possible 4-minterm groups. If a quad is found, its corresponding single-literal term (e.g., A, B', C) is added to the result, and its minterms are marked as "covered."
   • Pairs (Groups of 2): Next, it scans for all possible 2-minterm groups among the remaining uncovered minterms. If a pair is found, its two-literal term (e.g., A'B, BC') is added, and its minterms are covered.
   • Singletons (Individual Minterms): Finally, any minterms that could not be grouped are treated as individuals and their full three-literal term (e.g., A'B'C') is added to the result.
3. Output Formatting: The resulting terms are concatenated with + signs to form the final Sum-of-Products expression.

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📜 License

This project is licensed under the MIT License. See the LICENSE file for details.