Basic Data Types
In a computer, all data, even the instructions, is stored in a binary format. Binary data consist entirely of 1s and 0s, or, in the case of a computer, it could be represented as “on” and “off” for current in a circuit, or “positive” and “negative” charges stored on a magnetic storage device. It could even be “open” and “closed” for physical memory gates. There are many different ways to represent it, but it all boils down to just 1s and 0s.
Of course, we need a way to convert between the binary 1s and 0s that a computer understands and the actual data we’d like to represent. On this page, we’ll cover some of the common types of data and how they are handled by most computer programming languages.
Working with binary data can be a complex topic. In this program, we won’t deal directly with binary data very often. If you’d like to learn more about the binary numerical system and how it works, check out the Wikipedia article on Binary Numbers.
You may also want to review the List of Types of Numbers article as well, since we’ll refer to several of those types.
Binary literals are often prepended with 0b
thus 10
represents the decimal number 10, whereas 0b10
represents the binary number 10 and the decimal number 2. Recall that a literal represents the actual typed value.
Common Numerical data
Numbers, and thus numerical literals, are used everywhere in computer programs. This goes beyond obvious arithmetic and accounting applications. Modern graphics, artificial intelligence and simulation programs use numerical representations of data to quickly perform their operations. Thus, it is unsurprising that there are many ways to write and store numeric data.
Integers
The first type of data we’ll deal with in our computer program is whole numbers. These are numbers such as 1, 0, 1, 25, 186, 12852, and more. In both mathematics and programming, we refer to these numbers as integers. An integer is any whole number, or a real number without a fraction or decimal component. We sometimes refer to these numbers as counting numbers.
To store these numbers in our computer program, we typically use a signed integer data type. This data type allows us to store both positive and negative numbers in binary in our computer’s memory. We won’t go too far into the details of how that works in this course, but there is more information on how that works on Wikipedia
Floating Point
Next, we’ll also need to handle numbers that include a fraction or decimal component. These include rational numbers such as 1.5, 2.98, 3 1/3, and even irrational numbers such as $ e $ and $ \pi $.
Our computer uses a special representation known as floating point to store these numbers. Floating point is very similar to scientific notation, where a number such as 1,230,000 is represented as $ 1.23 * 10^{6} $. In this example, 1.23 is the significand and 6 is the exponent of the number. It is known as floating point because the decimal point “floats around” the number based on the exponent. We could represent the same number as $ 12.3 * 10^{5} $ or $ 0.123 * 10^{7} $ just by adjusting the exponent, causing the decimal point to move within the significand.
Modern computers use the IEEE 754 standard for encoding floatingpoint numbers into binary. Again, we won’t go into the specifics here, but the graphic below gives us a good idea of how a floating point number can be broken up and stored in binary.
Here we can see that a 64 bit space in memory is divided into three parts, one for the sign (to denote either a positive or negative number), another for the exponent, and a third for the fraction or significand of the number.
Just like there are rational numbers (such as 1/3) which cannot be exactly represented in the base 10 decimal number system, there are numbers which cannot be exactly exactly represented in base 2 (the underlying binary system used by a computer). In fact, there are many more rational numbers that cannot be exactly represented by binary numbers using floatingpoint than there are in a base 10 system.
In addition to this, because floats have a finite (set) number of bits, there is a limit to the number of significant bits we can use (typically 16 for a 64bit float). This is generally only a concern in scientific computing (where we are dealing with either very big or very small numbers). However, many programs use common graphic processing units, which use only 32bits (7 significant digits) to speed up calculations. This much lower accuracy can cause problems with statistical simulations.
Boolean
Boolean values, named for George Boole represent true
and false
in a computer program. While it may be as simple as storing a single bit, with 0 and 1 representing true
and false
, most programming languages provide a special way to deal with these values as they are very important in our computer programs. We’ll spend most of the next several chapters discussing how to work with Boolean values, but for now they are just another type of data our program could store.
Text as Data
Character
Many highlevel programming languages have a character data type. A character represents a single letter in a written language such as English. Most programming languages use a special code called ASCII, or the American Standard Code for Information Interchange. It defines a numerical value for each character in the English language, as well as several special characters such as the newline or \n
character we’ve already seen. Below is a table showing the entire ASCII code.
So, to store the character c
, our computer would store the number 99 in binary. We should also notice that the capital and lowercase letters are separate, so C
is 67.
Modern computer programming languages also support the use of Unicode characters. We won’t cover that in this course, but it is important to remember later on when working with languages other than English.
String
Sometimes we want to store entire sentences in our computer programs. A sentence is just a String of characters, objectoriented languages use a string class for this purpose and we’ll cover everything we need to know about strings in a later chapter.

File:IEEE 754 Double Floating Point Format.svg. (2015, January 21). Wikimedia Commons, the free media repository. Retrieved 20:50, December 18, 2018 from https://commons.wikimedia.org/w/index.php?title=File:IEEE_754_Double_Floating_Point_Format.svg&oldid=147276375. ↩︎

File:ASCIITablewide.svg. (2018, March 6). Wikimedia Commons, the free media repository. Retrieved 21:51, December 18, 2018 from https://commons.wikimedia.org/w/index.php?title=File:ASCIITablewide.svg&oldid=291044172. ↩︎