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PASCAL CH3: Arithmetic Operation 算術運算+ - PASCALChapter 3: Arithmetic Operation in PASCAL第三課：PASCAL的算術運算3.1 Arithmetic Operation算術運算Mathematical Operation數學運算PASCAL OperatorPASCAL 運算符Operation運算Example例子+Addition 加法5 + 121.2 + 3.4-Subtraction 減法4 23.2 2.1-Unary Minus 一元減法-4-8.8*multiplication 乘法4 * 87.2 * 1.2/Real Division實 數 除 法4 / 24.5 / 1.5DivInteger Division整 數 除 法23 div 3modModModulo ( Reminder )模數 ( 餘 數 )23 mod 3I. The operators can be use in numbers, constants and variables.以上的運算符可以用於數字、常量及變量。II. In an operation, it can have both integer type and real type variables:在運算過程中，可以同時包括整數及實數類：A. If in a operation have both integer and real data types, the output value must be ( real ) type.如果在一個算術運算中包括整數和實數類，其輸出結果一定是( 實 數 )類。B. If the operation involved / (real division), the output value must be real type.如果在運算式中掀涉 / (實數除法)，其輸出結果一定是實數。Operation運算Example例子Result結果Result Type (I: Integer 整數)結果類型 (R: Real Type 實數)+Addition加法123 + 321444I4.4 + 5.59.9R-Subtraction 減法369 123246I0.5 0.1450.355RMultiplication乘法11 * 555I2.4 * 0.51.2RReal Division實數除法600 / 2030.0R600.0 / 2.030.0R3.1.1 Unary Minus一元減法It is a sign to negate the value of an operand. For example,這是一個將數值改為其相反數值的符號。例如：1234 ( -1234 )3.1.2 Integer Division 整數除法The operand div to find the ( quotient ) of am integer division. The reminder will be neglected.其運算符是 div ，並用來找出整數除法的( 商 )，並捨去其餘數。Example例子Mathematical Operation數學運算Result結果25 div 7 3 Quotient 商7 )2521 4 Reminder 餘數3Expression 表達式Result結果5 div 808 div 518 div 5-1-8 div 5-1-8 div 518 div 0Undefined8.5 div 5Undefined3.1.3 Modulo Operation 模數(餘數)運算I. The operator mod is used to find the ( reminder ) in an integer division and the quotient will be neglected.運算元 mod 用作找出整數除的( 餘 數 )，並捨其商。II. This operation only allowed for ( integer ) and the divisor must not be ( zero ).此運算只可容許( 整 數 )，而且除數不可以是( 零 )。Expression 表達式Result結果5 mod 858 mod 538 mod 53-8 mod 5-3-8 mod 5-38 mod 808 mod 0UndefinedEvaluate the following arithmetic expression: 估計以下算術運算的答案：Arithmetic Expression算術運算Result 結果(3+4)*5-629-99 div 9-11-6 mod (2+4)0-(1998 mod 25) * ( 8 div 3 )-463.2Converting Mathematical Expression in PASCAL數學表式在Pascal 上的轉換Mathematical Expression數學表式PASCAL ExpressionPASCAL 表式5 9a2+b2a*a+b*b(F-32)5/9*(F-32)B2-4ACB*B-4*A*C10x310*x*x*xA(-(B/C)A*(-(B/C)a+bcd(a+b)/(c*d)(xy+z)2(xy+z)*(xy+z)a2+b2-4aca*a+b*b-4*a*c3.3 Precedence of Arithmetic Operators 算術運算符優先次序?3+4*5 7*5 353+4*5 3+20 23?When the arithmetic operation involve more than one operators, it is necessary to define clearly the precedence of arithmetic operators:當算術運算掀涉多過一個運算符時，便有需要義清楚運算符執行的優先次序：1.Operator with higher precedence will be evaluated first:先運算有較高優先次序的運算符：Level of Precedence 優先次序Operator運算符1( )2- (unary minus 一元減號)3* , / , mod, div4+, - (subtraction 減法)Example例子：Evaluation Step 運算步驟-X/(Y+Z)1.Value in parentheses括號內之數值+2.Unary minus 一元減號- 3.Real division 實數除法 /2.Operators with same precedence is evaluated from ( left ) to ( right ).若運算符先次序相同，則由( 左 )至( 右 )運算。Example例子：Evaluation Step 運算步驟4/A*C1.Real division 實數除法 / 2.Multiplication 乘數 * 3. Nested parentheses are evaluated from the ( inside out ).嵌套括號由( 內 至 外 )運算。Example例子：Evaluation Step 運算步驟(2 mod (3+4) div 61.Innermost parentheses最內的括號 +2.Outermost parentheses最內的括號 mod3.Integer division 整數除法 div3.4 Arithmetic Functions 算術函數I. Arithmetic function consists of two parts:數學函數包括兩個部份： A. function ( name )/函數( 名 ) sqrt(x) Compare比較： B. function( argument )/函數( 變 元 )II. There is no space between the function name and the parenthesis.函數名與括號之間沒有空格。ArithmeticFunction算術函數Purpose用途ArgumentType變數類型ReturnType轉回類型Example例子abs(x)Return ( absolute ) value of x.得出x的( 絶 對 )值。I / RSame asargument與變元相同abs(-3)3abs(3.5)3.5round(x)Round the x in the nearest integer.得出x四捨五入的值。I / RIround(2.1)2round(2.7)3round(2) 2sqrt(x)Return the ( square root ) of x.得出x 的的正( 平 方 根 )。I / R /+R / +sqrt(9) 3.0sqrt(2) 1.414trucn(x)Return the ( integer ) part of x.得出x的( 整 數 )部份。I / RI trunc(2.1) 2 trunc(5.9) 5 trunc(4) 4random(x)Return a number greater than or equal to zero, but less than x.得出一個大或等於零，但小於x的數。 0 random(x) x I / +I / + rand(3)I : Integer 整數R : Real 實數+ : positive number正數Example例子Program程式Output輸出Remarks備注abs(x)Program abcx;begin writeln(abs(123); writeln(abs(-456); writeln(abs(123.456):1:3); writeln(abs(-323.256):1:3); readln()end.123-456123.456-323.256round(x)program roundx;begin writeln(round(2.5); writeln(round(2.6); writeln(round(-2.5); writeln(round(-2.6); readlnend.23-2-3The PASCAL compiler we used (Bloodshed Dev-Pascal) is round off for value greater than 0.6.本校的Pascal編輯 (Bloodshed Dev-Pascal) 器是五捨六入。trucn(x)program truncx;begin writeln(trunc(2.5); writeln(trunc(2.6); writeln(trunc(-2.5); writeln(trunc(-2.6); readlnend.22-2-2sqrt(x)program sqrtx;begin writeln(sqrt(12); writeln(sqrt(25); writeln(sqrt(3*3+4*4); readlnend.3.46E+00005.00E+00005.00E+0000sqrt(-1) : Undefined未定義random(x)program random1;begin writeln(1st:, rand); writeln(2nd:, rand); writeln(3rd:, rand); writeln(4th:, rand); readlnend.When the function do not have argument type (x), it will return a real value between 0 and 1, that is:當此函數沒有變數類型(x)，會得出一個零與一之間的實數。即是： 0random1 program random2;begin writeln(random(100)+1); writeln(random(100)+1); writeln(random(100)+1); writeln(random(100)+1); readlnend.To generate an random integer, a integer argument n can be used and the vaule is:當要得出一個隨機整數，必需輸入一個整數變數n： 0random(n)n 3.5 Assignment Statement 賦值語句 Variable 變量x:=y( Expression 表 式 )The assignment symbol which mean “get the value of”.賦值符，指取其值為。Expression can be a number, ( variable ) or ( constant ).表式可以是數值，( 變 量 )或( 常 量 )。Example例子Result結果program assign1;const three = 3;var x, y, z : integer;begin x :=5; y :=x; z := three; writeln(x, y, z); readlnend.5 5 33.5.1 Assigning Integer and Real Values to Variables給變量賦予整數及實數值Integer can assign to integer and real variable, but real number can only assign to real variable.整數可以配給整數及實數的變數，但實