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13.1 IMPORTANT PROGRAMMING CONCEPTS
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TABLE 13-2 Hexadecimal values with binary and decimal equivalents. Note the $ in front of the hexadecimal number is used as an indicator like % for binary numbers. HEXADECIMAL NUMBER $0 $1 $2 $3 $4 $5 $6 $7 $8 $9 $A $B $C $D $E $F BINARY EQUIVALENT %0000 %0001 %0010 %0011 %0100 %0101 %0110 %0111 %1000 %1001 %1010 %1011 %1100 %1101 %1110 %1111 DECIMAL EQUIVALENT 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
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be able to perform some kind of arithmetic manipulation on the values (or data) before storing them into another variable (or even back into the same variable). To do this, a number of different mathematical operations are available in all high-level programming languages to allow you to modify the assignment statement with mathematical functions in the format
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DestinationVariable = SourceValue1 + SourceValue2
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in which DestinationVariable is loaded with the sum of SourceValue1 and SourceValue2. DestinationVariable must be a variable, but SourceValue1 and SourceValue2 can be either constants or variables. Their values are read by the computer, stored in a temporary area within the processor, added together, and the result (sum) is stored into the destination variable. Along with being able to add two values together, programming languages provide a number of different mathematical (addition, subtraction, multiplication, and division) operations that can be performed on variables as well as bitwise (AND, OR, XOR) and compari-
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PROGRAMMING FUNDAMENTALS
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son (equals, less than, greater than, etc.). Table 13-3 lists the commonly used mathematical operations in computer programming. The characters used to represent the different operations may have some differences between languages, but for the most part they are quite consistent for the basic mathematical operations. Multiple operations can be performed from a single expression, resulting in a very complex mathematical process being carried out within the computer from a string of characters that were quite easy for you to input into the computer program. 13.1.4.2 Order of Operations All but the oldest or very simple programming languages can handle more than one operator in an expression. This allows you to combine three or more numbers, strings, or variables together to make complex expressions, such as
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5 + 10 / 2 7
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This feature of multiple operators comes with a penalty, however. You must be careful of the order of precedence or operation, that is, the order in which the program evaluates an expression. Some languages evaluate expressions using a strict left-to-right process (the Parallax BASIC Stamp 2 PBASIC language is one), while others follow a specified pattern where certain operators are dealt with first, then others. This is known as the order of operations and ensures that the higher priority operations execute first. The common order of operations for most programming languages is listed in Table 13-3. The programming language usually does not distinguish between operators that are on the same level or precedence. If it encounters a _ for addition and a - for subtraction, it will evaluate the expression by using the first operator it encounters, going from left to right. You can often specify another calculation order by using parentheses. Values and operators inside the parentheses are evaluated first. Keeping the order of operations straight for a specific programming language can be difficult, but there is a way of forcing your expressions to execute in a specific order and that
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TABLE 13-3 or Priority PRIORITY Lowest
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Different Mathematical Operators and Their Order of Operations
ORDER 1 2 3 4 5 6
OPERATORS (negation), (bitwise not), !(logical not) + (addition), (subtraction) * (multiplication), /(division) &(bitwise AND), |(bitwise OR), ^(bitwise XOR) <<(shift left), >>(shift right) <(less than), <=(less than or equals), =(equals), !=(not equals), >(greater than), >=(greater than or equals)
Highest
&&(logical AND), (logical OR)
13.1 IMPORTANT PROGRAMMING CONCEPTS
is to place parentheses around the most important parts of the expression. For example, if you wanted to find the product of 4 and the sum of 5 and 3 and store it in a variable, you could write it as
A = 4 (5 + 3)
in your program to ensure that the sum of 5 and 3 is found before it is multiplied by 4. If the parentheses were not in place, you would probably have to use a temporary variable to save the sum before calculating the product, like
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