barcode print in asp net VISUAL BASIC FUNDAMENTALS in Visual Studio .NET

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VISUAL BASIC FUNDAMENTALS
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[CHAP. 2
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2.6 HIERARCHY OF OPERATIONS Questions in meaning may arise when several operators appear in an expression. For example, does the expression 2 * x 3 * y correspond to the algebraic term (2x) (3y) or to 2 (x 3y) Similarly, does the expression a / b * c correspond to a/(bc) or to (a/b)c These questions are answered by the hierarchy of operations and the order of execution within each hierarchical group. The hierarchy of operations is 1. 2. 3. 4. 5. Exponentiation. All exponentiation operations are performed first. Multiplication and division. These operations are carried out after all exponentiation operations have been performed. Multiplication does not necessarily precede division. Integer division. Integer division operations are carried out after all multiplication and (ordinary) division operations. Integer remainder. Integer remainder operations are carried out after all integer divisions operations. Addition and subtraction. These operations are the last to be carried out. Addition does not necessarily precede subtraction.
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Within a given hierarchical group, the operations are carried out from left to right.
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EXAMPLE 2.10
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The arithmetic expression
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a / b * c
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is equivalent to the mathematical expression (a/b) c, since the operations are carried out from left to right. Similarly, the arithmetic expression
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b ^ 2 4 * a * c
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is equivalent to the mathematical expression b2 (4ac). In this case, the quantity b ^ 2 is formed initially, followed by the product 4 * a * c [first 4 * a, then (4 * a) * c]. The subtraction is performed last, resulting in the final numerical quantity (b ^ 2) (4 * a * c).
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A more extensive listing of the Visual Basic operators and their respective hierarchical ordering is given in 3.
2.7 INSERTING PARENTHESES We may wish to alter the normal hierarchy of operations in a numeric expression. This is easily accomplished by inserting pairs of parentheses at the proper places within the expression. Then the operations within the innermost pair of parentheses will be performed first, followed by the operations within the second innermost pair, and so on. Within a given pair of parentheses, the natural hierarchy of operations will apply unless specifically altered by other pairs of parentheses embedded inside the given pair. Remember to use pairs of parentheses. A careless imbalance of right and left parentheses is a common error among beginning programmers.
EXAMPLE 2.11
Suppose we want to evaluate the algebraic term
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VISUAL BASIC FUNDAMENTALS
[ 2(a + b)2 + (3c)2 ] m / (n+1)
A Visual Basic expression corresponding to this algebraic term is
(2 * (a + b) ^ 2 + (3 * c) ^ 2) ^ (m / (n + 1))
If there is some uncertainty in the order in which the operations are carried out, we can introduce additional pairs of parentheses, giving
((2 * ((a + b) ^ 2)) + ((3 * c) ^ 2)) ^ (m / (n + 1))
Both expressions are correct. The first expression is preferable, however, since it is less cluttered with parentheses and therefore easier to read.
2.8 SPECIAL RULES CONCERNING ARITHMETIC EXPRESSIONS Special problems can arise if an arithmetic expression is not correctly written. Such problems can be avoided by remembering the following rules. 1. Preceding a variable by a minus sign is equivalent to multiplication by 1.
EXAMPLE 2.12
The arithmetic expression
x ^ n
is equivalent to (x ^ n) or 1 * (x ^ n), since exponentiation has precedence over multiplication. Hence, if x and n are assigned values of 3 and 2, respectively, then x ^ n will yield a value of 9.
Except for the condition just described, operations cannot be implied.
EXAMPLE 2.13
The algebraic expression 2 (x1 + 3x2) must be written in Visual Basic as
2 * (x1 + 3 * x2)
Note that the multiplication operators must be shown explicitly. Thus, the arithmetic expressions 2 (x1 + 3 * x2) and 2 * (x1 + 3 x2) are incorrect.
In an expression involving exponentiation, a negative quantity can be raised to a power only if the exponent is an integer. (Do not confuse the exponent in an arithmetic expression with the exponent that is a part of a single- or double-precision real constant.) To understand this restriction, we must see how exponentiation is carried out. If the exponent is an integer quantity, the quantity to be exponentiated is multiplied by itself an appropriate number of times. But if the exponent is not an integer quantity, Visual Basic computes the logarithm of the quantity being exponentiated, multiplies this logarithm by the exponent, and then computes the antilog. Since the logarithm of a negative number is not defined, we see that the operation is invalid if the quantity being exponentiated is negative.
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