feat(conversions): Add Binary and Gray Code conversion algorithms

[JDeep1234]

Description

This PR adds comprehensive Binary Gray Code conversion utilities to the conversions module.

Gray Code (also known as reflected binary code) is a binary numeral system where two successive values differ in only one bit. This property makes it particularly useful in:

• Error correction and detection
• Digital communications
• Rotary position encoders
• Analog-to-digital converters
• Karnaugh maps in digital logic design

What's Added

New File: conversions/binary_to_gray_code.py

4 Functions implemented:

1. binary_to_gray(binary_number: int) -> int

   • Convert binary number to Gray Code using XOR operation
   • Formula: gray = binary XOR (binary >> 1)

2. gray_to_binary(gray_number: int) -> int

   • Convert Gray Code back to binary
   • Uses iterative XOR with right-shifted values

3. decimal_to_gray(decimal_number: int) -> str

   • Convert decimal to Gray Code binary string representation
   • Combines decimalbinaryGray Code conversion

4. gray_to_decimal(gray_string: str) -> int

   • Convert Gray Code binary string to decimal
   • Includes binary string validation

Features

Comprehensive Testing

• 39 doctests covering all functions
• Tests for valid inputs (0, 1, 2, 4, 7, 10, 15, 255...)
• Tests for edge cases (0, negative numbers, floats)
• Tests for error handling (TypeError, ValueError)
• All tests passing locally

Code Quality

• Passes ruff check (no linting errors)
• Passes python -m doctest -v (39/39 tests pass)
• Python 3.13+ compatible
• Type hints for all parameters and return values
• PEP 8 compliant naming conventions

Documentation

• Detailed docstrings for every function
• Wikipedia reference included
• Clear explanation of Gray Code properties
• Usage examples in doctests
• Interactive demonstration in __main__

Error Handling

• Validates input types (must be int for numeric functions)
• Validates input values (must be non-negative)
• Validates binary strings (only '0' and '1' allowed)
• Meaningful error messages for invalid inputs

Example Usage

`python
from conversions.binary_to_gray_code import binary_to_gray, gray_to_binary

Binary to Gray Code

binary_to_gray(10) # Returns: 15 (binary 1010 Gray 1111)

Gray Code to Binary

gray_to_binary(15) # Returns: 10 (Gray 1111 binary 1010)

Decimal to Gray Code string

decimal_to_gray(7) # Returns: '100' (decimal 7 Gray Code 100)

Gray Code string to Decimal

gray_to_decimal('100') # Returns: 7
`

Verification Table

Decimal	Binary	Gray Code
0	0000	0000
1	0001	0001
2	0010	0011
3	0011	0010
4	0100	0110
5	0101	0111
6	0110	0101
7	0111	0100

Checklist

• I did my work - no plagiarism
• Work will be distributed under MIT License
• Code follows repository styles and standards
• New implementation (not duplicate of existing code)
• Python 3.13+ syntax
• Descriptive function and variable names
• Python naming conventions (snake_case)
• Type hints included
• Comprehensive doctests
• All doctests pass locally
• Passes ruff check
• Wikipedia reference included
• Proper input validation and error handling
• File name uses snake_case: binary_to_gray_code.py
• Fits into existing directory structure (conversions/)
• Code compiles and runs successfully

Related Issues

This adds a new algorithm that was not previously in the repository. Gray Code conversion is a fundamental algorithm in digital systems and complements the existing conversion utilities.

---

Hacktoberfest 2025 Contribution