Prerequisites:
- None, although some knowledge of Binary would be useful (Guide: HERE)
Terminology
Data types: A representation of the type of data that can be processed, for example Integer or String
Integer: A number that has no fractional part, that is no digits after the decimal point
Two’s Complement: The complement of a binary number with respect to 2^n
Integers:
A simple definition:
An Integer is a whole number. This means that 0, 3, 10, 12932 and -12 are all Integers, meaning that Integers can be both positive and negative numbers.
However, since Integers are whole numbers this means that the lack decimal places.
Integers are commonly used in programming languages, and we will see some ways that they are used below.
Integer Arithmetic
Integers can be used with multiplication, division addition and subtraction. These actually work as you would expect:
1+3 = 4
2 * 5= 10
19–3 = 16
However, Integer division is a little different. Since Integers don’t have decimal places usually the result is truncated to produce an Integer.
That is,
25 / 2 = 12
Uses in programming languages
Within programming languages Integers are extremely common data types and here are some common uses:
Incrementing Integers in a for loop
A common use for an Integers is for an index in a for loop
Java: For loop
for (int i = 1; i < 5; i++) {
System.out.println(i);
}JavaScript: For loop
var i;
for (i = 0; i < 5; i++) {
console.log(i)
}Python: For loop
for i in range(0, 3):
print(i)Swift: For loop
for i in 1...5 {
print(i)
}Memory usage of Integers
Integers are typically 4-bytes and can store both positive and negative numbers, although this varies in particular programming languages.
Since 4 bytes is equivalent to 32-bit numbers from 0 to 4294967295
The Integers 1 to 4 could be stored in the following binary pattern
Now it is possible that the order is reversed:
Negative values
In practice it is possible to store negative numbers by using the first bit as a sign bit.
The first bit can be 0 for positive numbers and 1 for negative numbers,
This action limits the numbers that can be stored to between -2147483648 and 2147483647.
Larger Integer values
On 64-bit machines Integers may be stored in 8-bytes of memory.
Conclusion:
Integers are particularly important in programming, as they are the usual way to store whole numbers, and that is something that invariably you will want to do.
If you want to store larger Integers you might think about using larger memory (for example use double the memory), storing Integers as floating numbers (possibly introducing precision inaccuracies) or even using arbitrary precision arithmetic which uses a flexible amount of memory per Integer but takes longer to produce the answer to calculations.
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