Análisis e implementación de operaciones aritméticas en base diez sobre dispositivos de lógica programable - Vázquez, Martín Osvaldo (2018)
General purpose microprocessors available on today's market does not provide hardware support for performing mathematical operations based on decimal representation. Instead, those chips implement arithmetic units using binary representation which provide a better performance. This fact is due to the two-state nature of electronic transistors. However, many commercial and scientific applications strictly requires computed calculations to be exactly the same as human performed. Actually, those systems that does not provide decimal floating point support, must adapt theirs operands to be computed assuming a difference with the real result. Errors inherited by precision loss may violate legal conditions, cause millionaire losses and even human life risk. The first alternative to smooth this is to give a special treatment to floating point operations at software level. This solution avoids result errors but increases computing resources and deteriorates calculation speed. A second popular alternative requires operands and result conversion from/to radix-10 and using the traditional computation. However, successive conversions could fall into precision loss. The decimal floating point arithmetic boosts the IEEE 754-1985 floating point standard adding decimal representation support and leading to IEEE 754-2008. The new standard states storage formats and treatment algorithms for handling decimal floating point numbers.There is a special interest on using FPGA programmable devices as hardware accelerators performing decimal floating point operations that meet IEEE 754-2008. This work proposes the analysis, design and implementation of different algorithms to solve arithmetic operations based on radix-10 and targeted to Xilinx programmable devices. The addessed operations are: addition, subtraction, square root and decimal logarithm. The fundamental aim of this work is to promote the design and implementation of both soft and firm cores of arithmetic units that meet IEEE 754- 2008 standard. A secondary intent is to establish synthesis strategies to be used on Xilinx tools for implementing electronic devices that supports radix-10 arithmetic operations.