CPS120: Introduction to Computer Science

Lecture 8

Comparing the Conventions

Bit Pattern UnsignedSign-

Magnitude1's

Complement2's

Complement000 0 0 0 0001 1 1 1 1010 2 2 2 2011 3 3 3 3100 4 -0 -3 -4101 5 -1 -2 -3110 6 -2 -1 -2111 7 -3 -0 -1

Sign-magnitude Operations

• Addition of two numbers in sign-magnitude is carried out using the usual conventions of binary arithmetic– If both numbers are the same sign, we add their

magnitude and copy the same sign– If different signs, determine which number has the

larger magnitude and subtract the other from it. The sign of the result is the sign of the operand with the larger magnitude

– If the result is outside the bounds of –2 n+1 to +2 n-1 –1, an overflow results

Two’s Complement Convention

• A positive number is represented using a procedure similar to sign-magnitude

• To express a negative number1. Express the absolute value of the number in binary2. Change all the zeros to ones and all the ones to zeros (called

“complementing the bits”)3. Add one to the number obtained in Step 2

– The range of negative numbers is one larger than the range of positive numbers

– Given a negative number, to find its positive counterpart, use steps 2 & 3 above

Two’s Complement Operations

• Addition:– Treat the numbers as unsigned integers

• The sign bit is treated as any other number

– Ignore any carry on the leftmost position

• Subtraction– Treat the numbers as unsigned integers– If a "borrow" is necessary in the leftmost place,

borrow as if there were another “invisible” one-bit to the left of the minuend

Overflows in Two’s Complement

• The range of values in two’s-complement is –2 n+1 to +2 n-1 –1

• Results outside this band are overflows

• In all overflow conditions, the sign of the result of the operation is different than that of the operands

• If the operands are positive, the result is negative

• If the operands are negative, the result is positive

One’s Complement

• Devised to make the addition of two numbers with different signs the same as two numbers with the same sign

• Positive numbers are represented in the usual way

• For negatives– STEP 1: Start with the binary representation of the

absolute value– STEP 2: Complement all of its bits

One's Complement Operations

– Treat the sign bit as any other bit– For addition, carry out of the leftmost bit is

added to the rightmost bit – end-around carry

Error Detection: Even Parity

• Bytes Transmitted

• 01100011

• 11100001

• 01110100

• 11110011

• 00000101 Parity Block

B

I

T

• Bytes Received

• 01100011

• 11100001

• 11111100

• 11110011

• 00000101 Parity Block

B

I

T

A Simple C++ Program

Comments //Simple C++ Program

//

// Purpose: To demonstrate the

// parts of a simple C++ program

Compiler Directive #include <iostream.h>

Main Function main ( )

Braces {

Statements cout << "This is a simple program ";

return 0;

}

Sample CommentsAt the start of the program

/**************************************************

** Miles Per Gallon **

** Programmer: Paul J. Millis **

** Purpose: Calculate mile per gallon and price per mile **

** given miles, gallons and gas price **

*************************************************/Within specific lines of code

float PricePerMile = 0.00; //store the price per mile

float MilesPerGallon = 0.0; //stores the miler per gallon achieved

Compiler Directives

• Instructions to the compiler rather than part of the C++ language– Most common directive is #include

• For Example: #include <iostream.h>– A .h file is a header file. It serves as a link between

program code and standard C++ code needed to make programs run

Functions

• A function is a block of code that carries out a specific task

• Every C++ program has a main function that executes when a program initiates– Includes open parenthesis to designate a

function– Ends with a return 0; statement

Braces

• Mark the beginning and ending of blocks of related code– Every opening brace must have a closing brace

Semicolons

• There must be a semicolon after every statement– To tell the compiler that the statement is

complete– Function definitions and compiler directives are

exempt

Uppercase or Lowercase

• Be careful to use the same combination of uppercase or lowercase lettering when you enter source code

• Commands and other reserved words are all lower case

Variables

• Used to store values in virtually every computer program– Used for “remembering” things during

program execution– Variables have names, types and values

• Values can change during execution

Data Types - Whole Numbers

• To store whole numbers in a variable, we use a variable of the int data type. – An int variable uses 4 bytes of memory. – An int variable can store a number as low as

-2,147,483,648. – An int variable can store a number as high as

2,147,483,647.

Data Types - Decimal Numbers

• To store decimal numbers in a variable, we use a variable of the double data type– A double variable uses 8 bytes of memory– A double variable can store a number as low as

-1.7 x 10308– A double variable can store a number as high

as 1.7 x 10308– A double variable can store a number with up

to 15 digits of precision (significant digits)

Data Types - Characters

• To store a letter or a single character (such as #, $, *, etc.), we use a variable of the char data type. – A char variable only uses 1 byte of memory. – A char variable can only hold one letter, digit,

or character.

Data Types – Words / Phrases

• To store a word or phrase (string value), we use a variable that is a string– Technically string is not a data type– You can think of it as a data type for now

Data Types – True and False

• The data type bool is useful to store true and false values

• Alternatively, we can simply use an int variable with either a 1 value (to represent true) or a 0 value (to represent false) if necessary

Other Data Types

• unsigned char, short, unsigned int, long, and unsigned long for whole numbers

• float and long double for decimal values

Using Variables in C++

• Variables must be declared before they are used in C++. Get into the habit of doing this at the top of your functions

char grade; // a students semester grade

int numStudents; // number of students in our class

double price; // price of item

string userName; // user's name

Variable Names

• Variable names are technically known as identifiers

• Choose your own variable names but you must be careful to use valid ones. Otherwise, the compiler will be confused and errors will result. When choosing your variable names:– do not use keywords that are defined in the

programming language (Reserved Words)– do not include spaces or other disallowed characters– do not use more than 31 characters– do begin the identifier with a letter

• Remember, C++ is completely case sensitive

Common Reserved Words

• break

• case

• char

• const

• default

• do

• double

• else

• extern

• float

• for

• if

• int

• long

• return

• switch

• void

• while

Conventions for Naming Variables• Use a conventional method of making your

variables easy to read at a quick glance. For example:

1. Begin variable identifiers with lowercase letters (eg. score)

if you wish to use more than one word within the identifier, you must capitalize the following words or parts of words (eg. semesterGrade, testScore)

2. Separate successive words with underscore characters ( _ ) (eg. semester_grade, card_value)

3. Hungarian notationBegin with type (eg. iTestScore)

Initializing Variables• C++ does not automatically initialize all variables

to the value 0 • If you do not initialize a variable to a certain value,

the variable will have an indeterminate value that can corrupt the logic of your program– You should usually initialize your variables at the same

time that you declare them. This is done with a declaration statement that is also an initialization statement

int numberOfPizzas = 3;          double monthlyCarPayment = 685;char letterGrade = 'A';string firstName = "Paul";

Constants

• Sometimes you need to use the same value many times throughout a program. In this case, it is proper to use a constant rather than a variable

• Constants allow you to give a name to a value used several times in a program

• The value never changes

Use of Constants (Literals)• Numeric

53.14159-17.29

• Characters'a''7''*'

• Strings (a sequence of symbols"I will be an better person "

Naming Constants

• Constants are defined in a way that is similar to variables– Select a data type and give the constant a name

• Any valid identifier name can be used to name a constant– Start with letter or underscore– Can’t use reserved words

Conventions for Naming Constants

• Traditionally, all uppercase letters have been used when naming constants

• Use the underscore character ( _ ) between consecutive words. This allows other programmers to be able to "pick out" your constants at a quick glance– Examples:

const double PI = 3.14159const double PA_SALES_TAX = 0.06const int SPEED_OF_LIGHT = 299792458; // commas can't be used here

Type Compatibilities

• You cannot store a value of one type in a variable of a different type – a type mismatch occurs

• You can typecast– Supply the name of the data type you want to

use to interpret the variable followed by the variable placed in parenthesis

• C = PI * float (diameter);

Common Arithmetic Operators

+ for addition

- for subtraction

* for multiplication

/ for division

% for modulus (like finding the remainder of a division problem)

Order of Operations

• Obey the order of operations– Perform the following mathematical operations in this

order: Parentheses, Exponentiation, Multiplication, Division, Addition and Subtraction

– Multiplication and division are of equal precedence, so you must work left to right within an algebraic expression

– The modulus operator (%) has the same precedence as * and / but is higher in precedence than + and -.

– Addition and subtraction work left to right within an algebraic expression as well

– Use parentheses if necessary to override the order of operations in order to produce the desired result