An operator is referred to as binary if it operates on two operands.
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: PRINT 125 + 4088 In TransactSQL, you can also perform the addition on text. Here is an example: PRINT 'Henry ' + 'Kono' 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 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.
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: PRINT 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: PRINT 128  42  5 PRINT 5  42  128 This would produce: 81 165 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 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: PRINT 128 * 42 This would produce 5376
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: PRINT 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.
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: PRINT 128 % 42 This would produce 2.
Like most computer languages, TransactSQL uses parentheses 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: PRINT (154  12) + 8 PRINT 154  (12 + 8) This would produce: 150 134 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. Here is another example of a nested SELECT statement that uses parentheses: SELECT (SELECT 448.25 * 3) + (SELECT 82.28  36.04); GO
When you use a value in your database or application, the value must be stored somewhere in the computer memory using a certain amount of space. A value occupies space that resembles a group of small boxes. In our human understanding, it is not always easy to figure out how a letter such as as B is stored in 7 seven small boxes when we know that B is only one letter. Bit manipulation or a bit related operation allows you to control how values are stored in bits. This is not an operation you will need to perform very often, especially not in the early stages of your database. Nevertheless, bit operations (and related overloaded operators) are present in all or most programming environments, so much that you should be aware of what they do or what they offer. One of the operations you can perform on a bit consists of reversing its value. That is, if a bit holds a value of 1, you may want to change it to 0 and viceversa. This operation can be taken care of by the bitwise NOT operator that is represented with the tilde symbol ~ The bitwise NOT is a unary operator that must be placed on the left side of its operand as in ~Value Here is an example: PRINT ~158 To perform this operation, the TransactSQL interpreter considers each bit that is part of the operand and inverts the value of each bit from 1 to 0 or from 0 to 1 depending on the value the bit is holding. This operation can be resumed in the following table:
Consider a number with a byte value such as 248. In our study of numeric systems, we define how to convert numbers from one system to another. Based on this, the binary value of decimal 248 is 1111 1000 (and its hexadecimal value is 0xF8). If you apply the bitwise NOT operator on it to reverse the values of its bits, you would get the following result:
The bitwise & is a binary operator that uses the following syntax Operand1 & Operand2 This operator considers two values and compares the bit of each with the corresponding bit of the other value. If both corresponding bits are 1, the comparison produces 1. Otherwise, that is, if either bit is 0, the comparison produces 0. This comparison is resumed as follows:
Imagine you have two byte values represented as 187 and 242. Based on our study of numeric systems, the binary value of decimal 187 is 1011 1011 (and its hexadecimal value is 0xBB). The binary value of decimal 242 is 1111 0010 (and its hexadecimal value is 0xF2). Let’s compare these two values bit by bit, using the bitwise AND operator:
Most of the times, you will want the interpreter to perform this operation and use the result in your program. This means that you can get the result of this operation and possibly display it to the user. The above operation can be performed by the following program: PRINT 187 & 242 This would produce 178
You can perform another type of comparison on bits using the bitwise OR operator that is represented by . Its syntax is: Value1  Value2 Once again, the interpreter compares the corresponding bits of each operand. If at least one of the equivalent bits is 1, the comparison produces 1. The comparison produces 0 only if both bits are 0. This operation is resumed as follows:
Once again, let’s consider decimals 187 and 242. Their bitwise OR comparison would render the following result:
You can also let the compiler perform the operation and produce a result. Here is an example: PRINT 187  242 This would produce 251
Like the previous two operators, the bitwiseexclusive OR operator performs a bit comparison of two values. It syntax is: Value1 ^ Value2 The compiler compares the bit of one value to the corresponding bit of the other value. If one of the bits is 0 and the other is 1, the comparison produces 1. In the other two cases, that is, if both bits have the same value, the comparison produces 0. This operation is resumed as follows:
We will again consider decimals 187 and 242. Their bitwiseexclusive XOR comparison would render the following result:
If the interpreter performs this operation, it can produce a result as in the following example: PRINT 187 ^ 242; This would produce 73. 


