Abstract
Abstract
The IEEE 754 Floating Point Standard, established in 1985, has been the predominant method for representing real numbers in computing systems. However, this standard encounters challenges such as precision errors and limitations in numerical range. This thesis introduces and examines the Symmetric Level Index (SLI) Arithmetic as a potential alternative, offering an extended numerical range compared to the IEEE 754 standard. Our research delves into the application of an existing hybrid framework that combines SLI and Floating-Point (FP) arithmetic. This hybrid framework is tested through various computational experiments, including the Conjugate Gradient Method(CG) for solving linear systems, the evaluation of the Softmax Function, and Automatic Differentiation (AD) computations.