The Suranadira Quantitative Symbolic System (QSS) introduces a novel framework for encoding and decoding information based on an extended binary system. Unlike traditional binary systems, it employs “affirmation” (01) and “negation” (011) functions to create two-dimensional, positionally decoupled truth patterns. This paper explores the theoretical foundations of the system, including its encoding principles, constellation structures, and the introduction of phase rules that decouple adjacent positions in positional numeral systems. A three-step decoding methodology is presented, alongside practical applications in number theory, computer science, and artistic expression. The implementation of the Suranadira Composer software demonstrates its potential for generative art and music composition. A case study of the composition “Skinny Frog” highlights the system’s artistic capabilities. The paper concludes with a discussion of future research directions, emphasizing its interdisciplinary relevance.