The binary number representation has dominated digital logic for decades due to its compact storage requirements. An alternative representation is the unary number system: We use N bits, from which the first M are 1 and the rest are 0 to represent the value M/N . One-hot representation is a variation of the unary number system where it has one 1 in the N bits, where the 1’s position represents its value. We present a novel method that first converts binary numbers to unary using thermometer (one-hot) encoders and then uses a “scaling network” followed by voting gates that we call “alternator logic,” followed by a decoder to convert the numbers back to the binary format. For monotonically increasing functions, the scaling network is all we need, which essentially uses only the routing resources and flip-flops on a typical FPGA architecture. Our method is clearly superior to the conventional binary implementation: Our area×delay cost is on average only 0.4%, 4%, and 39% of the binary method for 8-, 10-, and 12-bit resolutions, respectively, in thermometer encoding scheme, and 0.5%, 15%, and 147% in the one-hot encoding scheme. In terms of power efficiency, our one-hot method is between about 69× and 114× better compared to conventional binary.

中文翻译：

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基于函数导数的并行一元计算

几十年来，由于其紧凑的存储要求，二进制数表示一直主导着数字逻辑。另一种表示是一元数系统：我们使用ñ位，其中第一个米为1，其余为0代表值月/月. One-hot 表示是一元数系统的一种变体，其中它有一个 1ñ位，其中 1 的位置代表它的值。我们提出了一种新颖的方法，首先使用温度计（单热）编码器将二进制数转换为一元，然后使用“缩放网络”，然后使用我们称为“交流发电机逻辑”的投票门，然后使用解码器将数字转换回二进制格式。对于单调递增的函数，我们只需要扩展网络，它本质上只使用典型 FPGA 架构上的路由资源和触发器。我们的方法明显优于传统的二进制实现：在温度计中，对于 8 位、10 位和 12 位分辨率，我们的面积×延迟成本平均仅为二进制方法的 0.4%、4% 和 39%编码方案，以及 one-hot 编码方案中的 0.5%、15% 和 147%。在电源效率方面，