This paper proposes a novel inverse-quantization (IQ) algorithm and specialized DSP instructions for IQ algorithms. Non-linear inverse quantization is essential in both MPEG-1 Layer-3 and MPEG-2/4 Advanced Audio Coding (AAC). The proposed algorithm is optimized for the non-linear inverse quantization. The proposed algorithm has moderate computational complexity and can achieve the minimum average error. Performance comparisons show a significant improvement compared with existing algorithms. Furthermore, we propose the specialized DSP instructions and their architecture that can efficiently support the proposed IQ algorithm and other IQ algorithms. The audio-specific instruction-set processor that we have previously implemented employs these instructions and their hardware.