Approximate computing has emerged as a novel paradigm for achieving significant energy savings by trading off computational precision and accuracy in inherently error-tolerant applications, such as machine learning, recognition, synthesis and signal processing systems. This introduces a new notion of quality into the design process. We are exploring such approaches at various levels. At the hardware level, we have studied fundamentally achievable quality-energy (Q-E) tradeoffs in core arithmetic and logic circuits applicable to a wide variety of applications. The on-going goal is fold such insights into formal analysis and synthesis techniques for automatic generation of Q-E optimized hardware and software systems.