A novel compression framework that represents neural network weights through bit-level indexing, achieving compression ratios up to 40× with minimal accuracy degradation. BIE operates by encoding sparse weight matrices as sets of bit positions where non-zero values occur, providing three encoding variants: binary encoding for maximum compression, bitplane encoding for balanced compression-accuracy trade-offs, and blocked encoding for improved cache locality. The framework includes optimized sparse matrix multiplication kernels using Numba JIT compilation, comprehensive benchmarking tools, and integration capabilities with popular deep learning frameworks. All experiments are fully reproducible using the provided source code and datasets.