**Infinite Power of Two Calculator** is a specialized, high-precision computational utility engineered in pure ANSI C that transcends the limitations of fixed-width integer types. Designed for systems programmers, mathematicians, and computer science educators, it implements a custom **Arbitrary-Precision Arithmetic Engine** capable of calculating 2ⁿ for indefinitely large exponents without overflow. The application represents big integers as dynamically allocated arrays of decimal digits, employing efficient carry-propagation algorithms to multiply by two in O(d) time per iteration, where d is the current digit count. Operating as a continuous event loop, it sequentially computes and prints 2⁰, 2¹, 2², … with real-time string conversion and formatted output, running until manually terminated via SIGINT. Built with strict memory management—explicit `malloc`/`free` lifecycle control, buffer-safe operations, and zero external dependencies beyond the standard C library—the tool compiles to a compact, portable binary (~20 KB) compatible with Windows, Linux, and macOS. Its modular architecture separates core bigint operations (`bigint_multiply_by_2`, `bigint_to_string`) from I/O handling, enabling straightforward extension to other arbitrary-precision computations. Ideal for demonstrating low-level memory management, algorithmic efficiency, or exploring exponential growth patterns, this project exemplifies disciplined systems programming. With deterministic performance, transparent source code, and MIT licensing, Infinite Power of Two Calculator invites customization, pedagogical exploration, or integration into larger mathematical toolchains—delivering reliable, keyboard-driven big integer computation with minimal overhead. 🔢🧮💻