The IEEE 754 floating-point standard is the bedrock of modern computing, but its structural requirements -- a hidden leading bit, Base-2 bit-level normalization, and Sign-Magnitude encoding -- impose significant silicon area and power overhead in massively parallel Neural Processing Units (NPUs). Furthermore, the industry's recent shift to 8-bit formats (e.g., FP8 E4M3, OCP MX formats) has introduced a new hardware penalty: the strict necessity of Block-Scaling (AMAX) logic to prevent out-of-bound Large Language Model (LLM) activations from overflowing and degrading accuracy. The AetherFloat Family is a parameterizable architectural replacement designed from first principles for Hardware/Software Co-Design in AI acceleration. By synthesizing Lexicographic One's Complement Unpacking, Quad-Radix (Base-4) Scaling, and an Explicit Mantissa, AetherFloat achieves zero-cycle native integer comparability, branchless subnormal handling, and a verified 33.17% area, 21.99% total power, and 11.73% critical path delay reduction across the multiply-accumulate (MAC) unit. Instantiated as AetherFloat-8 (AF8), the architecture relies on a purely explicit 3-bit mantissa. Combined with Base-4 scaling, AF8 delivers a substantially wider dynamic range, acting as a ``Block-Scale-Free'' format for inference that circumvents dynamic scaling microarchitecture. Finally, a novel Vector-Shared 32-bit Galois Stochastic Rounding topology bounds precision variance while neutralizing the vanishing gradients that plague legacy formats. While AF16 serves as a near-lossless bfloat16 replacement via post-training quantization, AF8 is designed as a QAT-first inference format: its Block-Scale-Free property eliminates dynamic AMAX hardware at the cost of requiring quantization-aware fine-tuning for deployment.