I want to formally write the equivalence classes of the following language: $ $ L_k = \{w \in \{0,1\}^*\mid\text{ the } k\text{-th bit of }w\text{ from the right is } 1\}$ $

I understand the definition of equivalence classes, yet struggle to come up with a clear intuitive answer.

The language is regular, therefore i’d expect finite equivalence classes.

It seems like the essence of the information I am looking for is only “what is the $ k$ -th bit from the right”, which means i want to focus my attention on suffixes in the form of $ \sigma y \in \{0,1\}^*$ where $ |y|=k-1$ , $ \sigma\in \Sigma$ .

I would highly appreciate some guidance that would build my intuition for finding equivalence classes in general, and in this specific case.