In this section, we will show you how numbers are represented as integers or floating-point numbers in computers. Numbers form the foundation of computers and programming. Everything in a computer is represented by the binary numbers, ones and zeroes. Today, we have 64-bit computers that enable us to have a 64-bit representation of integers and floating-point numbers naively in the CPU. Let's take a deeper look at how integers and floating-point numbers are represented in the following two sections.
When we talk about integers, denoted as Z, we are talking specifically about machine-precision integers that are represented exactly in the computer with a sequence of bits. Also, an integer is a number that can be written without a fractional or decimal component and is denoted as Z by convention. For example, 0 is represented as 000000..., 1 is represented as ...000001, 2 is represented as ...000010, and so on. As you can see from this pattern...