An Engineer's Journey in Mathland: Balanced Ternary System + 3-Valued Logic

The majority of today’s computers depend on the binary system and Boolean algebra as their mathematical foundation. In this book, we will discuss the balanced ternary system and 3-valued logic as the foundation of an alternative system, showing its advantages.During California’s rolling blackouts in the late 90s, a group of software engineers couldn’t find anything better to do than solving riddles. One of these riddles inspired the creation of a new numeral system. Later, the author found out it's already been invented, namely the balanced ternary system. A big disappointment.Luckily, not all of his work has been invented before. So, he continued the journey and the development which led to 3-valued logic, and bigger discoveries and developments.In part 1, the reader will follow the journey and the flow of thoughts of developing the balanced ternary system as if it wasn't developed already. Therefore, the reader will find some improved algorithms, such as the division algorithm. If the reader is already familiar with the balanced ternary system, he will enjoy the novel parts.In part 2, we start by borrowing definitions and functions from Boolean to 3-valued logic until we hit a roadblock, like many others before us. Then, we examine the problem with a new perspective that enabled us to come up with new equations and relationships. These equations and relationships take 3-valued logic to the next level of maturity and applicability.The “electronic” Implementation is considered part 3 and will have its own book.‘Hope you enjoy the journey and find it inspiring. Read more