Arithmetic Operators
Their Precedence
in
Visual Basic 6.0



The following table shows some of the Visual Basic arithmetic operators and specifies their precedence.  (Precedence tells us that to correctly evaluate the expression 3 + 4 * 2 you must first multiply 4 by 2 and then add the intermediate result to 3 to yield a final result of 11.  (This should be contrasted to the value 14 which you would get if you add 3 and 4 before multiplying by 2.)  The highest precedence operators (first to be performed) are at the top of the table.  As you move down the table, the precedence of the operators decreases.  Where two or more operators share the same precedence, they will always be evaluated from left to right.  Thus, 12 / 6 / 2 yields the result 1 because you first divide 12 by 6 to obtain the intermediate result 2.  This value is then divided by 2 to produce the number 1.  If you had first divided 6 by 2, you would get 3.  Then, dividing 12 by 3 would give you a value of 4.  Remember, when several operators have the same precedence, they are evaluated from left to right.  If you want an expression to be evaluated in an order that is different from that specified in the following table, you can always use parentheses to specify this.  For example, 4 + 2 * 3 - 6 evaluates to 4.  While, (4 + 2) * 3 - 6 evaluates to 12.  And, (4 + 2) * (3 - 6) evaluates to -18.  The precedence of arithmetic operators matters.  If you do not get it correct, you will get the wrong answers.
 
 
 

Operator
 Meaning
^
 Exponentiation -- raise to a power.  For example, 2 ^ 3 equals 8.
-
 Negation -- the following operand is to be multiplied by minus 1.  (i.e., interpreted as a negative value.)
* /
 Multiplication Division.
\
 Integer division -- truncation.  7 \ 3 equals 2.  8 \ 3 also equals 2.  Any fractional portion in the result is discarded.
Mod
 Modulus -- remainder.  Defined for integers, Mod returns the remainder.  For example, 17 Mod 9 equals 8.
+ -
 Addition Subtraction. 
&
 Concatenation.  Strictly speaking, this is a string operator.  However, it can be used in an arithmetic expression.  For example, 3 & 19 will return 319, while (3 & 19) + 4 will return 323.  Bear in mind that VB is a very forgiving language.  It will make every effort to convert a value to the approriate type to allow the program to continue.  Most programming languages will crash with a compile or execution error if you attempt to combine string concatenation with arithmetic operators.

All programming languages have precedence rules regarding the order in which arithmetic operators are performed.  You need to be aware of these rules in whatever language you are using.

Here's a test, what is value of the arithmertic expression:

-2 ^ 4


What about the expression

(-2 ^ 4)


And the expression

(-2) ^ 4


The results of evaluating these expressions might surprise you. The - operator to the left of the digit 2 specifies negation. In the first two expressions, the negation operator is evaluated only after all exponentiation is first performed. That means the first two expressions raise the numeric value 2 to the power 4. (Exponentiation before negation.) This yields an intermediate result of 16. Then, this value is negated resulting in the value of the first two expressions being -16. The third expression uses parentheses to change the normal precedence order. First, the value 2 is negated yielding the result -2. Raising -1 to the fourth power yeilds the value 16. You will find that using parentheses is a valuable tool in creating arithmetic expressions that produce the desired results.