Multi-Base Number System

A C99 project for parsing, displaying, and manipulating numbers in arbitrary bases (2-36) with support for decimal points and repeating decimals.

Features

• Multi-base support: Bases 2 through 36 (using digits 0-9 and letters A-Z)
• Decimal representation: Support for fractional parts (e.g., 1A.3F in base 16)
• Repeating decimals: Notation using parentheses (e.g., 1.(3) represents 1.333...)
• Negative numbers: Standard negative sign notation
• Input/Output symmetry: base#number format for both input and output
• Interactive REPL: Read-Eval-Print-Loop for easy experimentation
• Comprehensive validation: Extensive error checking with helpful messages

Number Format

Syntax

[base#][-]digits[.digits][(repeating_digits)]

Examples

• 123 - Decimal number (base 10, default)
• 16#1A3F - Hexadecimal number
• 2#1011.01 - Binary with decimal point
• 36#Z9A - Base 36 using letters
• -9.8 - Negative decimal
• 1.(3) - Repeating decimal (1.333...)
• 16#1A.3(45) - Hex with decimal and repeating parts

Output Format

Non-decimal numbers are displayed with the base# prefix:

> 16#FF
  16#FF
> 255
  255

Building

Requirements

• CMake 3.10 or higher
• C99-compatible compiler (GCC, Clang)
• Ninja build system (optional but recommended)

Build Steps

# Configure
cmake -G Ninja -DCMAKE_BUILD_TYPE=Debug -S . -B build

# Build
cmake --build build

# Or use the provided tasks
cmake --build build  # for the default build task

VS Code Tasks

The project includes pre-configured tasks:

• configure: Set up CMake build system
• build: Compile the project
• clean: Remove build artifacts

Usage

Running Tests

./build/math

This runs the built-in test suite with:

• 10 valid test cases (various number formats)
• 12 invalid test cases (validation checks)

Interactive REPL

./build/math repl

The REPL accepts numbers in base#number format:

=== Math REPL ===
Enter numbers in format: base#number (e.g., 16#1A.3(45))
Default base is 10 if no prefix (e.g., 123.45)
Type 'exit' to quit

> 16#1A.3(45)
  16#1A.3(45)
> 2#1011.01
  2#1011.01
> 123.45
  123.45
> exit
Exiting REPL

Code Structure

Core Types

typedef uint8_t glyph_t;   // Character representation (0-9, A-Z)
typedef uint8_t value_t;   // Numeric value (0-35)
typedef uint8_t base_t;    // Number base (2-36)

Main Data Structure

typedef struct {
  number_proto_t proto;      // Base number data (base, digits, length)
  bool is_negative;          // Sign flag
  size_t decimal_length;     // Number of decimal digits
  size_t repeating_length;   // Number of repeating digits
} number_t;

Key Functions

Parsing & Display

• initialize_number_from_string(str, base) - Parse formatted string into number_t
• display_number(num) - Print number with base# prefix
• value_to_glyph(value) - Convert numeric value to character
• glyph_to_value(glyph) - Convert character to numeric value

Memory Management

• allocate_number_array(base, length) - Allocate number structure
• deallocate_number(num) - Free allocated memory

REPL

• repl() - Interactive Read-Eval-Print-Loop

Validation

The parser performs comprehensive validation:

1. Negative sign must be at the start
2. Decimal point requires digits before and after
3. Repeating section must:
   • Come after decimal point
   • Be non-empty
   • Use matching parentheses
4. Character validation for the specified base
5. No nested parentheses
6. At least one digit required

Error messages are written to stderr with clear descriptions.

Development

Code Formatting

The project uses clang-format with LLVM style:

clang-format -i src/main.c

VS Code auto-formats on save for .c and .cpp files.

Debugging

GDB configuration is included in .vscode/launch.json:

• Pretty-printing enabled
• Debug build with -g -O0

Compilation Flags

• Standard: C99
• Warnings: -Wall -Wextra
• Build type: Debug (with symbols)

Future Enhancements

• EVAL step: Arithmetic operations in the REPL
• Base conversion: Convert between different bases
• Math operations: Addition, subtraction, multiplication, division
• Precision control: Configurable decimal places for repeating sections

License

MIT License - see LICENSE file for details.

This is free and open-source software. You are free to use, modify, and distribute it without restriction.

Git History

Key commits:

• Initial implementation with parsing and display
• Memory allocation error handling
• Comprehensive input validation
• Invalid number representation (<<NaN>>)
• REPL functionality
• Base# prefix for input/output symmetry