Booth's Algorithm Simulation

This project provides a simulation of Booth's Algorithm for binary multiplication. The application allows users to input two numbers, and it will simulate the multiplication step-by-step using Booth's Algorithm. The results are displayed in a table, showing the state of each component (AC, Q, Q₁, and M) at each step.

Features

• User Input: Users can input two integers to multiply.
• Booth's Algorithm Steps: The algorithm is executed step-by-step, updating the AC, Q, Q₁, and M registers.
• Detailed Table Display: Displays the content of each register after every operation.
• Stylized UI: A responsive design with animations and interactive elements.

Table of Contents

• Features
• Installation
• Usage
• How It Works
• File Structure
• Limitations
• License

Installation

Clone the repository to your local machine:

git clone https://github.com/your-username/booths-algorithm-simulation.git
cd booths-algorithm-simulation

Open index.html in your browser to view and use the simulation.

Usage

1. Enter the First Number: In the "Enter First Number" field, input the first factor.
2. Enter the Second Number: In the "Enter Second Number" field, input the second factor.
3. Click Multiply: Press the "Multiply" button to start the Booth's Algorithm simulation.
4. View Results: The table will update with each step of the algorithm, showing the AC, Q, Q₁, and M registers and the operation performed.

How It Works

Booth's Algorithm uses a series of arithmetic operations and bit shifts to multiply two binary numbers. Here’s an overview of the algorithm as implemented in this project:

1. Initialize Registers: Initialize the AC (accumulator) to zero, set Q to the binary of the second factor, and set M to the binary of the first factor.
2. Bitwise Operations: Depending on the last bit of Q and the value of Q₁, perform arithmetic and logical operations:
   • AC = AC - M if Q₀ and Q₁ are 1 and 0, respectively.
   • AC = AC + M if Q₀ and Q₁ are 0 and 1, respectively.
   • Shift Right: Shift all bits of AC, Q, and Q₁ to the right.
3. Repeat for Each Bit: Continue this process until all bits are processed.
4. Display Results: After each operation, the contents of the registers and the operation performed are displayed in the table.

File Structure

• index.html: Contains the HTML structure and layout of the simulation.
• styles.css: Contains CSS styling for the application, including animations and responsiveness.
• script.js: Contains JavaScript logic implementing Booth's Algorithm and handling user interactions.

Example Output

For an input of factor1 = 5 and factor2 = -3, the table might display steps like:

AC	Q	Q1	M	Operation
00000000	1111	0	0001	Loading Data
...	...	...	...	Step-by-step output

Limitations

• Binary Representation: Only binary operations are shown; decimal output is not provided.
• Input Validation: Limited input validation—only integer inputs are supported.
• Complexity: The implementation is limited to Booth's Algorithm and does not cover other multiplication algorithms.

License

This project is licensed under the MIT License.