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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 make up  the given  number. For example, the decimal number ten is written as "$1010$" because it is $\underline{1}$ $\cdot$ $2^3+ \underline{0} $ $\cdot$ $2^2 + \underline{1} \cdot 2^1 + \underline{0} \cdot 2^0 $ $. Notice that this starts with the largest power of two.