Numerical Analysis - Python Codes

This repository contains Python implementations, exercises, and algorithms developed for the Numerical Analysis course.

Project Structure

Numerical-analysis-python-codes/
├── src/
│   ├── IEEE754.py
│   ├── main.py
│   ├── numpy_array.py
│   └── real_to_binary_converter.py
├── LICENSE
└── README.md

Contents

All scripts live in the src/ folder.

• IEEE754.py: IEEE754 class that converts a positive real number into the 16-bit IEEE 754 half-precision format (1 sign bit, 5 exponent bits with bias 15, 10 mantissa bits).
  • integer2binary / decimal2binary: static helpers that convert the integer and fractional parts into NumPy bit arrays (the fractional part is limited to 10 bits).
  • Attributes: sign_bit, integer_part, decimal_part, exponent_part.
  • print(obj) shows the full 16-bit pattern as sign|exponent|mantissa, with the leading 1 of the normalized number left out of the mantissa.
• main.py: Entry point that builds an IEEE754 object for 13.375 and prints its integer, decimal and exponent bits along with the final 16-bit representation.
• numpy_array.py: Creates an $n \times n$ matrix of random $d$-digit integers using NumPy and replaces its centered $m \times m$ subarray with -1.
• real_to_binary_converter.py: Converts integer (integer_to_binary), fractional/decimal (decimal_to_binary), and real floating-point numbers (real_to_binary) into fixed-point binary bit arrays using NumPy and math.modf.

Requirements

• Python 3.10+
• NumPy

Install the required dependencies via pip:

python -m pip install numpy

Usage

Clone the repository and run any script directly from the terminal:

git clone https://github.com/hamza-jpg/Numerical-analysis-python-codes.git
cd Numerical-analysis-python-codes
python src/main.py
python src/numpy_array.py
python src/real_to_binary_converter.py

Example Output (main.py)

$13.375 = 1101.011_2 = 1.101011 \times 2^3$, so the stored exponent is $3 + 15 = 18 = 10010_2$:

Integer part:  [1 1 0 1]
Decimal part:  [0 1 1]
Exponent part:  [1 0 0 1 0]
[0|1|0|0|1|0|1|0|1|0|1|1|0|0|0|0]

Sign	Exponent	Mantissa
0	10010	1010110000

Example Output (numpy_array.py)

Original array: 5 by 5:
[[42 17 89 34 56]
 [12 75 23 91 48]
 [64 38 10 52 79]
 [29 84 61 15 93]
 [50 19 47 82 31]]

Changed array: replaced by -1 from mid to 3 by 3 
[[42 17 89 34 56]
 [12 -1 -1 -1 48]
 [64 -1 -1 -1 79]
 [29 -1 -1 -1 93]
 [50 19 47 82 31]]

Example Output (real_to_binary_converter.py)

This is the integer part:  [0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1]
This is the decimal part:  [1 1 0 1 0 0 0 0 0 1 1 0 0 0 1]
[0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1] , [1 1 0 1 0 0 0 0 0 1 1 0 0 0 1]

📄 License

This project is open-source and licensed under the MIT License.