The good news -- logical operations are easy to understand and pretty easy write. The bad news -- they can get complex and some are difficult to get right. These notes points out half-a-dozen common mistakes (traps) made when people are writing conditions in C++.

Reading -- Pages 45-48

These three pages introduce some simple ideas that will be used in every program you will write. They (or similar ones) are used in every language.

Hint -- a few extra parenthesis make logical expressions easier to read

Comparison Operators -- page 45

Symbol	Meaning	true example	false example
<	less than	1<2	2<2
<=	less than or equal	1<=2	2<=1
==	equal to	1==1	1==2
!=	not equal to	1!=2	1!=1
>	greater than	2>1	2>2
>=	greater than or equal	2>=2	1>=2

Trap -- == vs =

Do not write something like this:

 		if( i = 1 )                   //ERROR

when you want to test for equality. The above compiles and runs but (1) the condition is always true and (2) it changes the variable i to be 1! Instead write

 		if( i == 1 )

Trap -- using == with doubles

You can not rely on "==" working with double length numbers because of rounding errors. The value of (x == y) when x and y are doubles is nearly always false. It is better to check to see if x and y are close togther. A test like

 		if ( fabs(x-y) <= EPSILON )

is usually what is needed -- where you choose EPSILON to be a constant small number set to an acceptable error.

 		const double EPSILON = 0.0000001;

Logical Operators -- and, or, not -- page 46

For historial reasons we have two notations for each logical operator.

Symbol	Word
&&	and
||	or
!	not

Proffesional C++ programers tend to use the symbolic form -- C/Java/PHP programmers don't have a choice. I plan to use the words. You can use which ever you like.

Hint -- Testing for divisibility

Many times a program will need to find out if one number is divisible by another. As a simple example is a number even or odd. The "%" operator is useD to calculate remainders after dividing. So we can use
1. number % divisor == 0

   to check if the number is divisible by the divisor. For example, you might write:

    	if( number % 2 == 0)

    		cout << number << "is even."<< endl;

    	else

    		cout << number << "is odd."<< endl;

   Complex Conditions

   Complex conditions turn up in the solutions of many problems. They can be challenging to code. For example, suppose that an int variable year holds the number of the year -- say 2008. We may need to calculate whether this is a leap year or not.

   Every body knows that if the year is divisible by 4 then we have a leap year:

    		year % 4 == 0

   but this is not quite right, because nowadays the rule is more complex. When the year is a century, because then we must check if the century is divisible by 4:

    		year % 100 == 0 and (year /100) % 4 == 0

   When the year is not a century we have.

    		year % 100 != 0 and year % 4 == 0

   Now we need to combine the two rules. In this case their is a leap year if either condition is true:

    		(year % 100 == 0 and (year /100) % 4 == 0)

    		or

    		(year % 100 != 0 and year % 4 == 0)

   In fact the exact rule is worse than this because the century condition was only introduced in different years depending on which country you are in... For more information check out the Wikipedia on the web.

   The above shows that real life can involve complex conditions. The income tax code provides many more complex examples. Many businesses have very complicated formulas for calculating discounts, wages, stocks, etc.. Analysing and coding these is very interesting.

   Hint -- lay out conditions tidily

   Trap -- English syntax != C++ syntax

   This is a classic error. You want to code
   1. x and y are both equal to 0

      so you write

   2. x and y == 0

      Sadly, in C++, this is wrong. In C++ it compiles and computes the wrong condition because of the design of C++ (see [ Strange Conditions ] below). The correct code is

       		(x==0) and (y==0)

      Trap -- range tests

      Suppose you want to test if x lies between 1 and 2 inclusive. The following

       		if( ( 1 <= x ) and (x <= 2) )

      will work but
   3. 1 <= x <= 2 is incorrect -- it compiles and does something quiet wierd. Again see [ Strange Conditions ] below.

      Trap -- Using and when or is needed

      English speakers can get confused and use and when they need or. The result is often an condition that is always false (and so useless).

      You have to be very careful working these out.

      The data type bool and the two logical constants -- true and false

      George Boole investigated "The Laws of Thought" and invented an algebra (Boolean Algebra) that is name after him. This was an algebra with two values -- true, false. In his honor the logical values in C++ are said to be of type bool.

      So far you have met int and double. Now you have met bool. You can have Boolean variables, and store the results of bool expressions for future use:

       		bool tooBig = (x >= 10000);

       ...

       		if( tooBig ) ...

      Introducing bool variables can simplify complex conditions and make your prgram more readable.

      Hint -- Use Boolean Algebra to simplify conditions

      The rules of George Boole's algebra are useful for simplifying C++ conditions. Here is a list of the rules you can use
   4. Boolean_Algebra::=following
      Net
      1. For p, q, and r boolean expressions.
      2. p and p == p.
      3. p and q == q and p.
      4. p and (q and r) == (p and q) and r == p and q and r.
      5. p and false == false.
      6. p and true == true.

      7. p or p == p.
      8. p or q == q or p.
      9. p or (q or r) == (p or q) or r == p or q or r.
      10. p or true == true.
      11. p or false == p.

      12. not (not p) == p.

      13. not ( p and q ) == (not p) or (not q).
      14. not ( p or q ) == (not p) and (not q).

      
      (End of Net Boolean_Algebra)
      
      

      Add to these the rules for negating comparisons

   5. negating_comparison_operators::=following
      Net
      1. For expressions x,y.
      2. not (x==y) == (x!=y).
      3. not (x!=y) == (x==y).
      4. not (x<=y) == (x>y).
      5. not (x<y) == (x>=y).
      6. not (x>=y) == (x<y).
      7. not (x>y) == (x<=y).

      
      (End of Net)
      
      Here is an example based on our old text book -- Horstmann.

      Suppose we are working for a catelog company that has complex rules for calculating discounts depending on the country and the state. Our program may include this code

       		if( not (country == USA and state != AK and state!=HI))

       			shipping_charge = 20.00;

      We can use Boolean algebra to simplify the condition:
      Let

      1. not (country == USA and state != AK and state!=HI)
      2. not (country == USA) or not ( state != AK) or not (state!=HI)
      3. country != USA or state == AK or state==HI
      
      (Close Let )
      So the following will do the same test, simpler:

       		if( country!=USA or state==AK or state==HI)

       			shipping_charge=20.00;

   Strange Conditions

   Any expression can be a condition in C++! In an if like this

    		if( e )

   the expression e is evaluated and if the value is 0 then the if treats it as false. If e is non-zero then it is taken to be true.

   This is why we do not express x and y are greater than 0 like this x and y > 0. C++ treats this as (x) and (y > 0) and this is true if x is not 0 and y is greater than zero.

   Similarly, C++ will convert a bool value into numbers:

   • false +> 0
   • true +> 1
   and this is why 1<=x<=2 does not test if x lies betweeen 1 and 2. Instead C++ treats this as (1<=x) <= 2 -- first the program tests if x is greater than 1 and if it is produces a 1, of false then it gets a 0. These are then compared to 2. The result is therefure true!

   The property that in C++ data becomes bool and vice versa is exploited when we test to see if an input has worked or not:

    		if ( cin >> something )

    		{ do something }

    		else

    		{ panic }

Are there times outside the lab when I am availabe

Look for my office hours -- this defines 4*50 minutes each week when I will be available in my office: Tu+Th 10:30-11:40 and Wedns 3-4:20.

How do you use SSH to log in to CSci.CSUSB



1. Download the installer.... see syllabus.
2. Execute it and you should get a couple of extra Icons.
3. Double click to get a terminal window
   The host is jbh3-1.csci.csusb.edu



What does using namespace std mean and why do we use it

A namespace is a collection of names. The namespace std contains many useful names including cout and cin. The using namespace allows us to write these without saying which namespace they are in.

The libraries that we #include are they real files

Yes. They are placed in /use/include in most UNIXes. Many of them are files with the extension '.h' for header. You get them from the same place as the compiler.

How do you code exponents in C++

Mathematical expressions x to the power y, for general y are written

 		pow(x,y)

using the <<cmath>> library. The mathematical exponential function e to the x can be written

 		exp(x)

using the smae library. The parentheses are essential.

How many libraries can you include in one program

As many as you want.

Can you have pi in a program without cmath

Only if you type in the value of π yourself

What is the reason that x and y == 0 is not (x==0) and (y==0)

Tradition.

What programs have logical expressions

Nearly every program needs conditions and the simplest way to write these is nearly always using logical operators.

What types of programs have truth tables

Not many..... BUT truth tables are a good way to think about complex conditions.

Can we use the comparison operators

Yes. Indeed you will and must use them:-)

When do use the not operator

You use it when you have written an expression but realise it is the oposite of what you wanted. The you put "not("...")" around it.

How many different comparison operators are in C++

6

How many different logical operators are in C++

3

How many must we know

All 3 logical operators, and all 6 comparison operators.

Are there only 3 logical operators in C++

Yes -- kind of. The 6 comparison operators can also be used to compare bool expressions. For example

p	q	P<q
false	false	false
false	true	true
true	false	false
true	true	false

What does bool mean

The reserved word bool in C++ is the name of a type of Boolean data.

Where do bool and get their names from.

The name bool comes from George Boole [ George_Boole ] who invented it in the 1800s.

The word int is shorthand for integer -- the mathematician's name for a whole(integral) number.

Are there other types we will learn about in class.

Yes: char, short, long, string, ..., arrays, vectors, ... enumerations, ...

plus the Do-It_Yourself data types: structs and classes.

When is bool used

The main use of the reserved word bool in C++ is to introduce variables that have two possible values: true and false. Absolutely typical is setting a flag to note something that has happened:

 		bool end_of_file_flag =false;

 		...

 			end_of_file_flag= (cin >> variable);

Why does not have a different priority to and and or

(1) not is a prefix operator. The other two are infix operators.

(2) The is a long long tradition of having not act on the following simple condition rather than a group:

 		not today and tomorrow

means:

 		(not (today)) and tomorrow

not:

 		not (today and tomorrow)

What does bool actually do

It reserves a piece of storage that can hold one of two values.

Is a while statement a kind of loop

Yes.

Is a while statement the same concept as a loop

No -- some loops are not while loops.

I dont understand while statements.

The will be covered in the next reading, lecture and lab. These should help.

1. and::="the bool conjunction operator",
2. (x and y) is true if and only if both x is true and y is true.
3. bool::="a type of data with two values true and false and three operators, and, or, not".
4. not::="the bool negation operator",
5. (not x) is true if and only if x is false.
6. or::="the bool disjunction operator",
7. (x or y) is true if and only if either x is true or y is true.

1. Complete the following truth tables:

   x	y	x and y	x or y
   true	true	?	?
   true	false	?	?
   false	true	?	?
   false	false	?	?

2. Trace the following program with several different input values: [ 05ex0.cpp ]