Extending the Digital Structure of the Binary Base Number System

In this article, I introduce a new set of numbers in base four, where the units are the standard binary digits and the first two prime numbers. These primes are considered "authentic" because they cannot be divided into any of their parts using basic arithmetic operations such as addition, subtraction and division. The digits of the enhanced number system are: 0, 1, 2, and 3. This forms a number system in base four. In a base-four number system, the binary exponentially doubles, so a quantity like 110 in base four is equivalent to 20 in the decimal system. In binary, it would only be 6. However, this has extraordinary technological implications that we must address because it will not be as simple as turning a switch on and off. It will pose a real challenge to our scientific and technological development. In this article, I introduce basic gate logic and the rules for arithmetic operations. Future articles will delve deeper into this topic.