Computer Science 1620

1
Computer Science 1620

• Arithmetic

2

• C Math
• we have seen how to use numbers in our program to
  represent data
• however, we can also manipulate this data
• we will look at some basic mathematical operators

3

• Operators
• there are five arithmetic operators

Operator Symbol
Addition
Subtraction -
Multiplication
Division /
Modulus
4

• Arithmetic Expression
• to use an arithmetic operator, use the following
  syntax

numeric expression
operator
numeric expression
A numeric expression is any expression whose
value is a number. This is also called an
operand.
Operator in this case refers to one of the 5
arithmetic operators.
5

• Arithmetic Expression
• Examples
• add 3 and 4
• subtract 40 from 75
• multiply 36 to 97
• divide 49 by 7

numeric expression
operator
numeric expression
3

4
75
-
40
36

97
49
/
7
In short, exactly the infix notation that you are
probably used to (just different symbols).
6

• The statement
• in C is an expression
• more specifically, an arithmetic expression
• the value of the expression is
• whatever the formula evaluates to
• in the above example, the value of the expression
  is 7

3 4
7

• Examples (from text)

Expression Value
2 5 7
13 89 102
34 20 14
45 90 -45
2 7 14
8

• Where are arithmetic expressions used?
• anywhere an expression is valid
• we have seen two places so far where an
  expression is valid
• in a cout statement
• in an arithmetic expression

9

• In a cout statement

include ltiostreamgt using namespace std int
main() cout ltlt "14 27" ltlt endl
cout ltlt 14 27 ltlt endl return 0
What will the output of this program be?
10
(No Transcript)
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• Why did we get this output?

include ltiostreamgt using namespace std int
main() cout ltlt "14 27" ltlt endl
cout ltlt 14 27 ltlt endl return 0
12

• Why did we get this output?

include ltiostreamgt using namespace std int
main() cout ltlt "14 27" ltlt endl
cout ltlt 14 27 ltlt endl return 0

• The first expression is a string literal,
  because of the quotation marks.
• Remember that the value of a string literal is
  the text between its quotation marks

13

• Why did we get this output?

include ltiostreamgt using namespace std int
main() cout ltlt "14 27" ltlt endl
cout ltlt 14 27 ltlt endl return 0

• The second expression is an arithmetic
  expression.
• Remember that the value of an arithmetic
  expression is the value of the formula.

14

• Quick Note More than one type of expression
  can be sent in the same cout command
• must be separated by ltlt operator

include ltiostreamgt using namespace std int
main() cout ltlt 3 ltlt "" ltlt 4 ltlt "" ltlt 34
ltlt endl return 0
Integer
String
Integer
String
Arith. Exp.
15
(No Transcript)
16

• Integer Division
• what is the output of the following program?

include ltiostreamgt using namespace std int
main() cout ltlt 5.0 / 2.0 ltlt endl
cout ltlt 5 / 2 ltlt endl return 0
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• Integer Division
• 5 / 2 2 (the quotient)
• when two integers are divided, the result is an
  integer
• when a fraction (or remainder) occurs, it is
  simply ignored
• note that this ONLY APPLIES TO INTEGERS
• doubles are computed as expected

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• Examples

Equation Result
14 / 7
-5 / 2
-7 / -3
19 / 20
19.0 / 20.0
2
-2
2
0
0.95
19

• Modulus
• the remainder of the division operation
• in mathematics, if we divide 34 by 5, we get

Remainder
Quotient
r 4

• in C
• integer division gives us the quotient
• modulus gives us the remainder

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• Modulus

include ltiostreamgt using namespace std int
main() cout ltlt 34 / 5 ltlt endl
cout ltlt 34 5 ltlt endl return 0
21

• Modulus
• has many uses in programming
• extracting digits
• determining a prime number
• hashing
• etc
• we will see modulus again when we reach
  conditionals

22

• Embedded Arithmetic Expressions
• recall the format of an arithmetic expression
• recall that a numeric expression is an expression
  whose value is a number
• since an arithmetic expression's value is a
  number, we can use it in another arithmetic
  expression

numeric expression
operator
numeric expression
3 4
23

• Embedded Arithmetic Expressions
• recall the format of an arithmetic expression
• recall that a numeric expression is an expression
  whose value is a number
• since an arithmetic expression's value is a
  number, we can use it in another arithmetic
  expression

numeric expression
operator
numeric expression
3 4
numeric expression
operator
numeric expression
1 2 4
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• Embedded Arithmetic Expressions
• previous slide formally demonstrates that C can
  handle expressions with more than one operator
• important this is nothing special, just one
  binary expression embedded in another
• each binary expression is executed individually

cout ltlt 1 2 4 ltlt endl
1 2 4

• This expression is evaluated first
• Its value becomes the operand for
• the second expression.

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• Order and Precedence
• there are two possible orders of computation in
  the previous expression

Order 1
Order 2
1 2 4
1 2 4
1 6
3 4
7
7
Which one does C use?
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• Order and Precedence
• there are two possible orders of computation in
  the previous equation

Order 1

• Rule
• arithmetic expressions are evaluated left to
  right when their operand is the same

1 2 4
3 4
7
27

• Order and Precedence
• the order of evaluation becomes important for the
  and / operators

Order 1
Order 2
1 - 2 - 4
1 - 2 - 4
1 - -2
-1 - 4
-5
3
28

• Order and Precedence
• what about when the operators are not the same?

Order 1
Order 2
1 2 4
1 2 4
1 8
3 4
12
9
Which one does C use?
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• Order and Precedence
• what about when the operators are not the same?

Order 2
RULE When different operands are
used, precedence rules take over. , /, are
evaluated before any , - operations
1 2 4
1 8
9
30

• Order and Precedence
• what about when the operators have the same
  precedence?

Order 1
Order 2
1 - 2 4
1 - 2 4
1 - 6
-1 4
3
-5
Which one does C use?
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• Order and Precedence
• what about when the operators have the same
  precedence?

Order 1
RULE When two arithmetic operands have the same
precendence, they are evaluated left to right.
1 - 2 4
-1 4
3
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• Order and Precedence
• what happens if I want the addition performed
  first?
• that is, parentheses override any precedence rule

1 2 4
(1 2) 4
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• Examples

Equation Result
3 4 5
(3 4) 5
8 / 2 4
8 / (2 4)
19 / 20 200
23
35
16
1
0
34

• Mixed Mode Expressions
• when two integers are used in an arith. exp., the
  value of the operation is an integer as well
• 5 2 7
• when two doubles are used in an arith. exp., the
  value of the operation is a double as well
• 5.0 2.0 7.0
• what happens when an integer and a double are
  used in an operation?
• 5.0 2 ????? 7 or 7.0?

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• Rules for Mixed Mode Arithmetic (text)
• if the operator has the same types, then the
  value of the expression has the same type
• if one of the operands is a floating point number
  and the other an integer, then the integer is
  promoted to a floating point number. The value
  of the expression is a floating point number
• the precedence rules from before still apply

36

• Evaluating mixed-mode expressions
• the rule is applied for each operation
  individually
• the type of the value of each expression must be
  remembered
• order of operations usual precedence and left to
  right rules

37

• Examples

Equation Result
3 / 2 5.5
15.6 / 2 5
4 5 / 2.0
4 3 7 / 5 25.5
4 3 / 5 3
6.5
12.8
6.5
-12.5
7