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$1$ $\underline{\text{Binary Notation}}$  \vspace{2mm}  We define binary numbers as the powers of two that lay the foundation for the additive building blocks of positive integers. In this system, integers are expressed in terms of only $0$s and $1$s. The values that make up each integer are the sum of the powers of two that go into the number. For example, the decimal number $10$ is written as $1010$ because