In literature, NAND and NOR are two logic gates that display functional completeness, hence regarded as Universal gates. So, the present effort is focused on exploring a library of universal gates in binary that are still unexplored in literature along with a broad and systematic approach to classify the logic connectives. The study shows that the number of Universal Gates in any logic system grows exponentially with the number of input variables $N$. It is revealed that there are $56$ Universal gates in binary for $N=3$. It is shown that the ratio of the count of Universal gates to the total number of Logic gates is $\approx $ $\frac{1}{4}$ or 0.25. Adding constants $0,1$ allow for the creation of $4$ additional (for $N=2$) and $169$ additional Universal Gates (for $N=3$). In this article, the mathematical and logical underpinnings of the concept of universal logic gates are presented, along with a search strategy $ULG_{SS}$ exploring multiple paths leading to their identification. A fast-track approach has been introduced that uses the hexadecimal representation of a logic gate to quickly ascertain its attribute.

翻译：文献中，NAND与NOR是两种具有功能完备性的逻辑门，被视为通用门。为此，本研究聚焦于探索文献中尚未涉足的二进制通用门库，并提出一种广泛且系统的逻辑联结词分类方法。研究表明，任意逻辑系统中的通用门数量随输入变量数$N$呈指数级增长。结果显示，$N=3$的二进制系统中有$56$个通用门，且通用门数量占逻辑门总数之比约为$\approx$$\frac{1}{4}$（即0.25）。通过引入常量$0,1$，可额外生成$4$个（$N=2$时）及$169$个（$N=3$时）通用门。本文阐述了通用逻辑门概念的数学与逻辑基础，并提出了搜索策略$ULG_{SS}$，通过多路径探索实现其识别。同时，引入了一种快速判定方法，利用逻辑门的十六进制表示快速确认其属性。