Unary and Binary Operators

This is the type of ruler we use to count numbers. It has a middle position of zero. The numbers on the left side of the 0 are referred to as negative while the numbers on the right side of the rulers are considered positive:

A value on the right side of 0 is considered positive. To express that a number is positive, you can write a + sign on its left. Examples are +4, +228, +90335. In this case the + symbol is called a unary operator because it acts on only one operand.

The positive unary operator, when used, must be positioned on the left side of its operand, never on the right side.

As a mathematical convention, when a value is positive, you do not need to express it with the + operator. Just writing the number without any symbol signifies that the number is positive. Therefore, the numbers +4, +228, and +90335 can be, and are better, expressed as 4, 228, 90335. Because the value does not display a sign, it is referred as unsigned as we learned in the previous lesson.

To express a variable as positive or unsigned, you can just type it. here is an example:

SELECT +1250

As you can see on the above ruler, in order to express any number on the left side of 0, it must be appended with a sign, namely the - symbol. Examples are -12, -448, -32706. A value accompanied by - is referred to as negative.

The - sign must be typed on the left side of the number it is used to negate.

Remember that if a number does not have a sign, it is considered positive. Therefore, whenever a number is negative, it MUST have a - sign. In the same way, if you want to change a value from positive to negative, you can just add a - sign to its left.

Here is an example that uses two variables. One has a positive value while the other has a negative value:

SELECT -1250

Binary Operators

The Addition

The addition, also called the sum, is an operation used to add one item to another. The addition is performed using the + sign. To get the addition of two values, you type + between them, as in Value1 to Value2. After the addition has been performed, you get a new value that you can make available or display to the user. You can perform the addition on two numbers. Here is an example:

SELECT 125 + 4088

You can also add more than two values, like a + b + c. The order you use to add two or more values doesn't matter. This means that Value1 + Value2 is the same as Value2 + Value1. In the same way a + b + c is the same as a + c + b the same as b + a + c and the same as c + b + a. This means that the addition is associative as illustrated in the following statement:

SELECT 128 + 42 + 5;
SELECT 5 + 42 + 128;
GO

-----------
175

(1 row affected)

-----------
175

(1 row affected)
1>

The Subtraction

The subtraction operation, sometimes called the difference, is used to take out or subtract one value from another value. It is essentially the opposite of the addition. The subtraction is performed with the - sign. Here is an example:

SELECT 1240 - 608

Unlike the addition, the subtraction operation is not associative. This means that a - b - c is not necessarily equal to c - b - a. This is illustrated in the following statements:

SELECT 128 - 42 - 5;
SELECT 5 - 42 - 128;
GO

Notice that both operations of the addition convey the same result. In the subtraction section, the numbers follow the same order but a different operation; and the last two operations render different results.

The Multiplication

The multiplication allows adding one value to itself a certain number of times, set by a second value. As an example, instead of adding a value to itself in this manner: a + a + a + a, since the variable a is repeated over and over again, you could simply find out how many times a is added to itself, then multiply a by that number which, is this case, is 4. This would mean adding a to itself 4 times, and you would get the same result. 

The multiplication is performed with the * sign. Just like the addition, the multiplication is associative: a * b * c = c * b * a. Here is an example:

SELECT 128 * 42

This would produce 5376

The Division 

The division operation is similar to cutting an item in pieces or fractions of a set value. Therefore, the division is used to get the fraction of one number in terms of another. The division is performed with the forward slash /. Here is an example:

SELECT 128 / 42

This would produce 3

When performing the division, be aware of its many rules. Never divide by zero (0). Make sure that you know the relationship(s) between the numbers involved in the operation.

The Modulo

In the above division, 128/42, the result is 3. When you multiply 42 by 3, as in 42*3, you get 126. In some cases, you may be interested in knowing the amount that was left out after the operation. The modulo operation is used to get the remainder of a division as a natural number. The remainder operation is performed with the percent sign (%). Here is an example:

SELECT 128 % 42

This would produce 2

Additional SQL Operators

Parentheses

Like most computer languages, you can use parentheses in a SQL statement to isolate a group of items that must be considered as belonging to one entity. For example, as we will learn soon, parentheses allow a function to delimit the list of its arguments. Parentheses can also be used to isolate an operation or an expression with regards to another operation or expression. For example, when studying the algebraic operations, we saw that the subtraction is not associative and can lead to unpredictable results. In the same way, if your operation involves various operators such as a mix of addition(s) and subtraction(s), you can use parentheses to specify how to proceed with the operations, that is, what operation should (must) be performed first. Here is an example:

SELECT ((154 - 42) + 8) As Number1;
SELECT (154 - (12 + 8)) As Number2;
GO

 Number1
 -----------
         120

(1 row affected)
 Number2
 -----------
         134

(1 row affected)

As you can see, using the parentheses controls how the whole operation would proceed. This difference can be even more accentuated if your operation includes 3 or more operators and 4 or more operands.