Ternary > Binary

This repository explores the implementation of ternary number systems in software, with the long-term goal of informing potential hardware designs.

This project does not claim that modern ternary systems are inherently superior to binary systems in practice.
Instead, it investigates the theoretical limits of information representation and compression, motivated by the fact that the most efficient radix in information theory is the irrational base e.
Since base e is not physically realizable, base-3 (ternary) is the most efficient practical integer approximation.

Binary

Computers all over the world use the binary system. in the binary system the computer uses 0 and 1 as truth values

-0 represents the off state of electrical appliances, -1 represents the on state of electrical appliances.

This system really stuck with the world because of its simplicity and its cheap cost implementation in hardware

Ternary

Soviets used the ternary system for their computers.

These computers were more efficient in processing data than their binary counterparts and often outperformed bitwise computers.
This is because the soviets used the balanced ternary system.
The components of the balanced ternary system.

• +1
• 0
• -1

Theory

1 Trit stores log₂(3) ≈ 1.585 bits of information while 1 Bit log₂(2) = 1 bit of information.

So ,in theory ternary system is more efficient in storing information. A single trit has three possible states, whereas a bit has two.

In information-theoretic terms:

• 1 bit stores 1 bit of information
• 1 trit stores log₂(3) ≈ 1.585 bits of information

This makes ternary systems theoretically more information-dense than binary, and base-3 is mathematically optimal among integer bases.

Design Decisions

This project intentionally takes several liberties for experimentation and clarity.

A chomp is defined as 9 balanced ternary digits (trits), forming a fixed-width ternary word:

• 9 trits = (3⁹ = 19,683) representable states as opposed to the 256 representable states of 1 Byte
• structured as three 3-trit groups
• conceptually analogous to the 8-bit byte in binary systems

A chip is defined as 3 balanced ternary digits (trits), forming a fixed-width ternary word:

• 3 trits = (3³ = 27) representable states as opposed to the 16 representable states of 1 Nibble
• structured as three 3-trit groups
• conceptually analogous to the 4-bit Nibble in binary systems

The term chomp and chip is a project-specific abstraction and is not a proposed standard.

Documentation

• Logical Operations
• Progenitor