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代数中很多问题的讨论是同所采用的数制无关的。而因为二进制具有运算简单、表达经济等优点,因此,对易于表为二进制的那些数学问题就应该考虑是否应基于二进制来进行研究以充分利用由此而带来的方便。本文只介绍一些背景不很复杂的实例,希望通过它们比较鲜明地表现出这种转换的基本方法和价值。此外,对以下所论及的几个熟知的数学问题,本文还提供了一些吸引人的新的证明方法和深入研究的途径。
The discussion of many problems in algebra is independent of the number system used. Because binary has the advantages of simple operation, economy of expression, etc., for those mathematical problems that are easy to express as binary, it should be considered whether the research should be based on binary to make full use of the convenience brought about by it. This article only introduces some instances where the background is not very complicated, and I hope to clearly demonstrate the basic method and value of this conversion through them. In addition, for several well-known mathematical problems discussed below, this article also provides some attractive new proof methods and in-depth research approaches.