The digits of the powers of 2

This thesis studies the large, small, and even digits that occur in the powers of 2. Large and small digits will be defined and some interesting properties will be studied.; In Chapter 2, a large digits Theorem is reviewed and studied in detail.; In Chapter 3, some applications of the outcome of the large digits Theorem are reviewed.; In Chapter 4, the natural density of the set S(x ) is presented and discussed.; In Chapter 5, the conclusion is presented with an exploration of open questions and related topics.