8 february 2013birkbeck college, u. london1 introduction to programming lecturer: steve maybank...

8 February 2013 Birkbeck College, U. London 1

Introduction to Programming

Lecturer: Steve Maybank

Department of Computer Science and Information Systems

sjmaybank@dcs.bbk.ac.ukSpring 2013

Week 5: Boolean Operations

Overview Java Lab 3, Exercises 2 and 4 Relational Operators Equality of strings Boolean operators De Morgan’s laws See Java for Everyone, Ch. 3

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Java Lab 3, Exercise 2 Integer calculations: write a

program that prompts the user for two integers and then prints

The sumThe difference…

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Keyboard Input

import java.util.Scanner;…Scanner in = new Scanner(System.in);System.out.print(“Please input an integer: ”);int i = in.nextInt();System.out.print(“Please input a second

integer: ”);int j = in.nextInt();

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Overflow Integers of type int must be in the range –231 to 231-

1. The following two integers are in this range:

int i=1500000000;int j = 1500000001;System.out.println(i+j);/* result: -1294967295 */System.out.println(i-j);/* result: -1 */

There are no error messages when i+j is evaluated.

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Java Lab 3, Exercise 4 Separate digits: write a program

that reads in a five digit positive integer and prints out the individual digits, separated by spaces. For example 16348 is printed out as 1 6 3 4 8

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Possible Solutions Input a five digit integer i Extract the digits, eg. d1=i%10; Print the digits and spaces. Alternative: use in.next() to input the five

digits of i in the form of a string. Divide the string into five substrings, one

for each digit. Reassemble the five substrings, with

spaces.

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Solution

String digits=in.next();String d1=digits.substring(0,1);String d2=digits.substring(1,2);String d3=digits.substring(2,3);String d4=digits.substring(3,4);String d5=digits.substring(4,5);String gap=“ “;String result =

d1+gap+d2+gap+d3+gap+d4+gap+d5;

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Relational Operators

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Java

Math

Description

> > greater than

>= greater than or equal

< < less than

<= less than or equal

== = equal

!= not equal

Relational Operator Examples

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Expression Value Comment

3 <= 4 true <= is less than or equal

3 =< 4 error Use <=

3 > 4 false > is the opposite of <=

4 < 4 false < is strict inequality

3 != 5-1 true != tests for inequality

1.0/3.0 ==0.33333333

false The numbers are similar but not equal

“10” > 5 error A string cannot be compared with a number

Precedence

Relational operators have a lower precedence than arithmetical operators, eg.

int floor = 10;boolean v = floor-1 < 13;

The expression floor-1 is evaluated first and the value is then compared with 13.

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Boolean Data Type A variable of type boolean has either

the value true or the value false, eg.boolean temp = true;

boolean is a reserved word, true and false are values.

It is not the case that true is 1 and false is 0.

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Boolean Operators

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Java Name Description

&& And Binary: a&&b is true if and only if a and b are both true.

|| Or Binary: a||b is true if and only if at least one of a, b is true.

! Not Unary: !a is true if and only if a is false.

Boolean Operator Examples

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Expression Value Comment

0<20 && 20<10 false Only the first condition is true

0<20 || 20<10 true The first condition is true

0<x<100 error 0<x has a boolean value, 100 is an integer

!(0<200) false 0<200 is true

frozen==true frozen No need to compare a boolean value with true

Combining Conditions Think carefully about the

difference between && and || Buying a shirt:

white, cotton, size 15 Buying apples:

from the UK, from France,from South Africa

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Lazy Evaluation of Boolean Expressions

Logical expressions are evaluated left to right. The evaluation stops as soon as the truth value is determined, eg.

int quantity = 0;boolean test1 = quantity > 0 && price/quantity < 10;/* test1 is false */boolean test2 = quantity == 0 || price/quantity < 10;/* test2 is true */

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Compile Time Errors

int temp = 40;boolean test1 = (0 <= temp <=100);/* 0<=temp is true, true<=100 is an error

*/

boolean test2 = (temp == 40||50);/* 40||50 is an error because || cannot be

applied to integers */

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Equality of Strings Use

boolean test = string1.equals(string2);

ExampleString str1 = “red”;String str2 = “blue”;System.out.println(str1.equals(str2));/* Prints: false */

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More on Equality of Strings str1==str2 returns true if and only if str1 and

str2 are initialised with the same string literal, eg.

String str1=“Rob”, str2=“Robert”;boolean test1=(str1==“Rob”); //trueboolean test2 = (str1==str2.substring(0,3)); //false

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Lexicographic Ordering

int sc=string1.compareTo(string2);

/* sc<0: string1 precedes string2 sc==0: string1 equals string2 sc>0: string1 follows string2

*/

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De Morgan’s Laws

Let a, b be Boolean variables. Then!(a && b) and (!a) || (!b)

have the same truth table.

Similarly!(a || b) and (!a) && (!b)

have the same truth table.

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Check the First Law Suppose a is false. Then

!(a && b) = !(false && b) = !false = true

(!a) || (!b)= (!false) || b = true||b = true

Suppose a is true. Then!(a && b) = !(true && b) = !b (!a)||(!b) = (!true)||(!b) = false||(!b)=!b

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Example of a De Morgan’s Law

Buying apples:

boolean reject1 = (!fromUK) && (!fromFR);

boolean reject2 = !(fromUK || fromFR);

/* reject1 has the same value as reject2 */

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Test Suppose that x and y are integers.

Test whether both of them are zero. Test whether at least one of x, y is

zero. Test whether exactly one of x, y is

zero. What is the value of !!(x>y)?

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