Field Programmable Gate Arrays (FPGAs) are increasingly being used for high-throughput floating-point computation. It is forecasted that by 2009, FPGAs will provide an order of magnitude greater sustained floating-point throughput than conventional processors. FPGA implementations of floating-point operators have historically been designed to use binary floating-point representations, as do general purpose processors. Binary representations were chosen as the standard over three decades ago because they provide maximal numerical accuracy per bit of floating-point data. However, the unique nature of FPGA-based computation makes numerical accuracy per unit of FPGA resources a more important measure of the usefulness of a given floating-point representation. From this viewpoint, higher radix floating-point representations are well suited to FPGA-based computations, especially high precision calculations which require the support of denormalized numbers. This work shows that higher radix representations lead to more efficient use of FPGA resources. For example, a hexadecimal floating-point adder provides a 30% lower Area-Time product than its binary counterpart, and a hexadecimal floating-point multiplier has a 13% lower Area-Time product than its binary counterpart. This savings occurs while still delivering equal worst-case and better average-case numerical accuracy. This work presents a family of higher radix floating-point representations that are designed specifically to interoperate with standard IEEE floating-point, allowing the creation of floating-point datapaths which operate on standard binary floating-point data, yet use higher radix representations internally. Such datapaths provide higher performance by any measure: they are more accurate numerically, consume less FPGA resources and have shorter latencies. When taking into consideration the unique nature of FPGA-based computing systems, this work shows that binary floating-point representations are not optimal for most FPGA-based arithmetic computations. Higher radix representations can therefore be a useful tool for building efficient custom floating-point datapaths on FPGAs.



College and Department

Ira A. Fulton College of Engineering and Technology; Electrical and Computer Engineering



Date Submitted


Document Type





FPGA, computer, arithmetic, floating-point, fixed-point, floating, fixed, point, radix, rounding, add, multiply, numerical, accuracy, throughput, latency, binary, hexadecimal, denormalized