Binary can be challenging. The values tend to have a lot of digits, long sequences of ones or zeros can be difficult to distinguish, and the relative magnitudes of multiple binary values can be difficult to resolve. In this episode, we discuss a couple of the popular methods to quickly represent binary in a more human readable form.

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An exploration of cinematography, societal expectations, and artist collaboration, “Fake It!” challenges the traditional definition of art. Part one follows the journey of creating a music video for an original song titled “Fake It!” by the band Model City. Location, lighting, camera, and editing choices are explained and connected to the song's themes of teenage angst, regret, and a rejection of societal norms. Part two explores the process of creating art by translating the hexadecimal color values from the music video into a new musical composition. This is accomplished through a mathematical process that converts the computer-identified RGB letters and numbers into notes on the musical scale.

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.