Blog Post 5

\(1\) \(\underline{\text{Binary Notation}}\)

We define binary numbers as the powers of two that lay the foundation for the additive building blocks of positive integers. Note that the word binary comes from “Bi” meaning two. In this system, integers are expressed in terms of only \(0\)s and \(1\)s. The values that represent each integer are calculated by finding the sum of the powers of two that make up the given number. We pull out the amount of times that each power of two occurs. 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. We read “\(1010\)” as “one-zero-one-zero” as opposed to one thousand and ten. The binary representation of the first few natural numbers are shown in the table below.

Pictured (above) is the binary representation of the numbers 1-8.