1. Modified from Sharon Guffy
Data Types
June 23, 2016
Amy Allen
Modified from Sharon Guffy

2. Data Types Overview Primitive data types Data structures Integers
Floating point numbers
Boolean
Characters
Data structures
Primitive types = data types (aka numeric types and characters)
Aggregate types: ordered or unordered
Brief discussion of how to make your own data types in some languages

3. Integers Number with no fractional part
Stores the exact value, so == comparisons are safe
Storage:
one bit to indicate if the number is positive or negative
a binary representation of the number
Absolute size limit (system-dependent)
E.g. a 32-bit system could store integers within ± ( )
Converting floating point numbers to integers truncates the decimal part (2.9 2, -2.1  -2)
Exact storage of the data, but this comes with a size limit
Relatively large (aka, 32 bit system has 31 bits to store the integer, 1 bit to store positive vs negative)
If you convert a number from float to integer, it will NOT ROUND, just truncates

4. Special types of integers
Long integers
Take up more space in memory than integers, but can store larger values
Short integers
Take up less space, but have smaller range
Unsigned integers
Same amount of space as integers
Only store integers >= 0
Useful for values that can never be negative (count, class size, etc.)
Can adjust the size limits of integers
Benefits/pitfalls to each size
Don’t want to store a small integer with a ton of space
Need to remember that a negative number should only be stored as a negative (otherwise problems can arise)

5. Integer Overflow Overflow: Integer exceeds its maximum/minimum size
Different systems deal with overflow differently
Some systems (e.g. R) may give you an overflow error
In other cases, values may wrap:
<largest possible positive integer> + 1 = <largest possible negative integer>
Others (e.g. Python) automatically convert to a long integer
How do these details affect you??
If size of integer is larger than limit: best thing to happen is an error. Worst thing to happen is a wrap-around
The computer doesn’t know what to do. Basically goes to the top limit and then retarts at the bottom (negative) limit
Language specificity with how the computer deals with problems
Example: Storing a positive (12) or negative (-12) as an UNSIGNED integer
Watch out for the giant number in place of the size that you expected

6. Floating point numbers
Numbers stored in scientific notation:
Sign
Power of ten
Binary representation of fractional part
i.e = +1.02*101
Double precision: Uses additional space, so it can store larger numbers and more decimal places
These are stored in your computer similar to how it is in scientific notation
Some number to store the exponent, some number to store the value, some number to store the sign
Typically size of storage is set to be muh larger than that of an integer
Remember, all restricted by storage size
Major problem will be accuracy of number storage. Because computer store everything as binary fraction
NOT ALL NUMBERS THAT CAN BE RECORDED IN BASE TEN CAN BE STORED IN BINARY
Type
Smallest Positive Value
Largest Value
Precision
float
⨉10-38
⨉1038
6 digits
double
⨉10-308
⨉10308
15 digits

7. Special floating point numbers
Special values
Inf (infinity) and –Inf (negative infinity)
NaN (not a number)—produced from operations without a definite answer (Inf/Inf, etc.)

8. Problems with floating point numbers
Since floating point numbers are stored as fractions in binary, not all numbers can be stored precisely, so math may not give exactly the answer you expect: >>> x = 3.2 >>> y = 1.1 >>> x+y == 4.3 False Hmmmm, that’s not right >>> x+y Therefore, it is best not to check equality of floating point numbers.
Think about storing 1/3 as a decimal x3 = NOT 1.0 as it should be
Remember the restrictions of the tools and rules of your language and number system

9. Boolean Used to store true/false values
Can be converted from any other type.
False values (may vary by language):
Numeric types: 0
Empty aggregate types ([], “”, {}, etc.)
All other values are true
Commonly used in loops and control structure
This is what your computer loves to store: 1 or 0, yes or no, on or off
Almost anything can be sored as a Boolean value
How the computer sees it
False: nothing, none, 0
True: something

10. Characters and Strings
Think of characters and strings and none numeric. A character is a single symbol and a string multiple symbols strung together
Differs significantly in Python and R
In Python characters are a string of length one
In R strings are still considered under character class

11. Data Structures Overview
A particular way of organizing data in a computer so that it can be used efficiently
Range from very basic to very complicated
Can be as simple as an ordered list of numbers
Can be more complicated like a graph

12. Why is all of this important?
You want to make sure you are storing and accessing your data as efficiently as possible.
You need to understand the pit falls of the data types and data structures you’re using so you can trouble shoot errors.