Chapter 3 - Notes Input/Output

Transcription

1 Chapter 3 - Notes Input/Output I. I/O Streams and Standard I/O Devices A. I/O Background 1. Stream of Bytes: A sequence of bytes from the source to the destination Types of Streams: i. Input Stream: A sequence of characters from an input device to the computer. ( Usually the keyboard ) ii. Output Stream: A sequence of characters from the computer to an output device. ( Usually the monitor ) 3. Every C++ Program must use the header file iostream and it contains two data types: i. istream ( input stream ) ii. ostream ( output stream ) 4. The header file also contains two variable declarations: i. cin ( common input ) a. Variables of the type istream are called input stream variables ii. cout ( common output ) a. Variables of the type ostream are called output stream variables iii. A stream variable is either an input or output stream variable. B. cin and the Extraction Operator Page 1

2 1. cin is a variable and >> is an extraction operator 2. >> is a binary operator and therefore requires two operands i. cin is the left hand operand and works as an input stream variable ii. The right hand side of the extraction operator must be a variable because the purpose of an input statement is to read and store values into a memory location and only variables refer to a memory location. 3. A single cin statement can read in more than one variable: Example: cin >> num1 >> num2 ; i. Every occurrence of >> extracts the next data item from the input stream. ii. The following statements are the same: cin >> num1 >> num2 ; or cin >> num1 ; cin >> num2 ; 4. The extraction operator >> skips all whitespace characters when scanning for input. i. Whitespace characters: Blanks, tabs, newline characters, and certain nonprintable characters. ii. Therefore, the following statement cin >> num1 >> num2 ; would properly read any of the three example inputs from the screen ( Assuming num1 and num2 were declared as integers ): and 67 separated by a single blank space and 67 separated by a several blank spaces and 67 separated by a tab space and 67 separated by a carriage return/line feed Page 2

3 Now num1 = 12 and num2 = How does the extraction operator determine what data type is being entered? cin >> X ; i. Suppose the user types in 2. Does the user want the number 2 or the character two. ii. The variable on the right hand side of the operator determines whether the 2 is retrieved as a number or a character. a. If the variable was declared as a data type int, it will be stored as a number. b. If the variable was declared as a char data type, it will be stored as a character. ii. What if the user types in 25? a. If the variable was declared as an integer data type, it will save the number 25. b. If the variable was declared as a float or double, it will save the number c. If the variable was declared as a character data type, it will save only the digit 2. Valid Input for a Variable of a Simple Data Type Data Type char int float or double Valid Input One printable character except the blank space An integer, possibly preceded by a ( + or - ) sign. A decimal number, possibly preceded by a ( + or - ) sign. If the actual data input is an integer, the input is converted to a decimal number with the zero decimal part. C. What if the User doesn't type the input properly? Page 3

4 1. What if the user types in more data than the program has variables? i. Once the variables in the cin statement are filled, it ignores and discards any other data the user may have typed in. 2. What if the user enters an integer for a float or double variable? i. It is not necessary for the user to type in a decimal for a float or double variable. The program will convert the integer to a decimal number before storing it in the variable. 3. What happens if the user enters a character for an integer variable or a decimal number for an integer variable? i. Entering a character into a variable declared as an integer during a cin statement causes an error called an input error. 4. What happens when the user enters a non-numeric character into an integer variable? i. The program enters a fail state when a non-numeric character is entered for an integer. The input operator immediately ceases and the program skips to the next line of code. It may appear on your screen as if nothing went wrong, but if you look at your output, you will find errors. II. Using Predefined Functions in a Program A. Predefined Functions: A set of instructions that performs a defined task, and is pre-written and available in a library that must be included with the source code. 1. A function, other than the main function, is normally called from the main function. This is known as a function call. Example: #include <cmath> Page 4

5 float base, exponent ; cout << "Please enter a number for the base of the power function: " ; cin >> base; cout << "Please enter a number for the exponent of the power function: " ; cin >> exponent; cout << endl; cout << base << " taken to the power of " << exponent << " = " << pow(base, exponent) << endl; 2. In the function call pow(base, exponent), pow is the function name and refers to the set of instructions that execute the power function. 3. The variables or values inside of the parenthesis are called arguments or parameters. This particular function requires two arguments or parameters. pow( 2, 3 ) Function call Arguments or parameters Function name 4. To use a predefined function in a program, you must know the following: i. The name of the header file to be included in your program. ii. iii. iv. The name of the function. This also means the exact spelling, etc. The number of parameters (arguments) the function takes. The data type of each parameter. v. What does the function do? What is its purpose? Will it return a value? 5. I/O provides several useful functions that can be called with the Page 5

6 iostream header file and using namespace std. These are functions that the programmer will use frequently but would be difficult to write for themselves. B. cin and the get Function 1. Remember that the use of cin and the extraction operator ( >> ) does not allow the programmer to store any whitespace ( blanks, tabs, or newline characters) into a character variable. But what if you need or want to store these characters? Example: Suppose the following code is written, char ch1, ch2 ; int num ; cin >> ch1 >> ch2 >> num ; During execution of the code, the user enters the following information: A 25 This is what happens: A gets stored in the memory space called ch1. 2 gets stored in the memory space called ch2. 5 gets stored in the memory space called num. This is not what you, the programmer, intended. You wanted ch1 to store A, ch2 to store the blank space, and num to store the integer cin.get( charvariable ) i. This is a function provided by the iostream header files. It allows the programmer to grab one character at a time from the input device (keyboard - shown on monitor) even if it is a whitespace character (blank, tab, newline character). ii. Notice that this function statement requires one argument or parameter. That parameter/argument is a character variable to store a character data type that will be extracted from the input. Page 6

7 iii. Notice the period between cin and get. This is called a dot rather than a period when used outside string notation. When used this way ( cin.get( chvar )), it is known as dot notation and becomes an operator called the member access operator. Suppose we now have the following code, char ch1, ch2 ; int num ; cin.get ( ch1 ) ; cin.get ( ch2 ) ; cin >> num ; During execution of the code, the user enters the same information: A 25 This is what happens: A gets stored in the memory space called ch1. a blank gets stored in the memory space called ch2. 25 gets stored in the memory space called num. iii. You cannot use the cin.get ( ) function statement with a data type argument of integer or float because it will give you a compiler error. C. cin and the ignore Function 1. cin.ignore ( intexpression, charexpression ); i. Allows the program to ignore or skip a designated number of characters. ii. iii. intexpression represents a variable or integer number of the amount of characters you would like to skip or ignore. charexpession represents a variable of type character or character that you would like to skip up to. Page 7

8 iv. In other words, if the statement cin.ignore( 5, 'A' ); was in your code, it would skip the next five characters in the input line unless one of those characters was a letter A. If no letter (or character) A was found in the next five characters, it would take the sixth character regardless of what it is ( assuming you have code that wants to take the sixth character ). v. Remember that a '\n' is a character. You could skip all the characters of a line until you got to the new line character. vi. An example of how it works: Suppose you have the following line of code: cin >> letr1 >> letr2 ; cin.ignore ( 100, '\n' ); cin >> letr3 ; And the user puts the following input on the screen: ghwyrkhlhj385609gjr98 7lkvcywhgn The result will be the following: 2 is stored in variable letr1 4 is stored in variable letr2 7 is stored in letr3 then the cursor waits at the character following the 7. D. The putback and peek Functions 1. putback Function: Allows the programmer to put back into the input stream the last character extracted from it by the get function. i. The syntax for this function: istreamvar.putback( ch ) ii. iii. istreamvar would be the cin variable, since we haven't covered any others yet. ch is the variable you stored the character from the get function. Page 8

9 iv. Here's an example of how to use it: Suppose you have the following line of code: cin >> letr1 >> letr2 ; cin.ignore ( 100, '\n' ); cin.putback ( letr2 ); cin >> letr3 ; And the user puts the following input on the screen: ghwyrkhlhj385609gjr98 7lkvcywhgn The result will be the following: 2 is stored in variable letr1 4 is stored in variable letr2 4 is put back on the input stream 4 is stored in variable letr3 then the cursor waits at the character peek Function: Allows the programmer to see or copy what the next character in the input stream is without taking it off of the input stream. i. The syntax for this function: ch = istreamvar.peek( ) ii. iii. iv. istreamvar would be the cin variable, since we haven't covered any others yet. Notice there is no required argument or parameter inside the parenthesis. You must include the parenthesis, however, you just don't have to put anything between them. The function cin.peek( ) returns a character. Because of this, you must store the character in a variable or print it to the screen like the following examples: cout << "The next character in the istream is: " << cin.peek( ) ; letr1 = cin.peek( ); Page 9

10 v. Now let's see how it works: Suppose you have the following line of code: cin >> letr1 >> letr2 ; cin.ignore ( 100, '\n' ); letr3 = cin.peek ( ); cin >> letr4 ; And the user puts the following input on the screen: ghwyrkhlhj385609gjr98 7lkvcywhgn The result will be the following: 2 is stored in variable letr1 4 is stored in variable letr2 7 is stored in variable letr3 7 is stored in variable letr4 then the cursor waits at the character after 7. III. Input Failure A. Input Failure: An attempt to read invalid data. For example, trying to read a character value into an integer variable. 1. Fail State: When input failure occurs, the input stream enters the fail state in which all further I/O statements using that stream are ignored. WARNING: The program then continues to execute with whatever values are in the variables and will produce incorrect results!! B. The clear Function: Restores the Input Stream to a working state. 1. Syntax and Use: istreamvar.clear( ) Page 10

11 Example of Use: int a = 23, b = 34 ; cout << "Enter a number followed by a character: " ; cin >> a >> b; cout << endl << "a = " << a << ", b = " << b << endl ; cin.clear ( ) ; // Restores istream in case of input failure cin.ignore ( 200, '\n' ) ; // Essentially skips to the next line cout << "Enter two numbers: " ; cin >> a >> b; cout << endl << "a = " << a << ", b = " << b << endl ; IV. Output and Formatting Output A. Manipulators used in the output stream require a preprocessor directive with the following header: B. setprecision: Controls the number of floating numbers output. Default output in some SDK's is 6 or scientific notation or E1 1. Syntax and Use: cout << setprecision( n ); 2. Example: Page 11

12 float num1, num2 ; cout << "Please enter two float numbers: " ; cin >> num1 >> num2; cout << endl; cout << setprecision(5) << num1 << " "; cout << setprecision(2) << num2 << endl << endl; Please enter two float numbers: e e Notice that the output is not in decimal format and that the amount of numbers displayed (not counting the e+006) is the same amount as the number in setprecision( n ). Also notice that the numbers were rounded off before being displayed. C. fixed: Forces the output of floating point numbers to be displayed as decimal point numbers. If an integer number is input as a float, it will add a decimal point and zeros afterward. ( NOTE: The manipulator showpoint does this also with integer input for float.) 1. Syntax and Use: cout << fixed; 2. Example of Use: float num1, num2 ; cout << fixed ; cout << "Please enter two float numbers: " ; cin >> num1 >> num2; Page 12

13 cout << endl; cout << num1 << " " << num2 << endl << endl; Please enter two float numbers: Notice that the integer number 12 has a decimal point and zeros in the output. Also notice that the first and second number have a precision of 8 numbers. This is evidently the default precision for this compiler. 4. What if we want to control the amount of numbers after the decimal point like in monetary output. This requires the use of setprecision( ) with the fixed manipulator. Example: float num1, num2 ; cout << fixed << setprecision(2) ; cout << "Please enter two float numbers: " ; cin >> num1 >> num2; cout << endl; cout << num1 << " " << num2 << endl << endl; Page 13

14 Please enter two float numbers: Notice that the setprecision( ) manipulator combined with the fixed manipulator controls only the amount of digits after the decimal point. 6. To undo the fixed manipulator, issue the following command: cout.unsetf ( ios :: fixed ) ; D. showpoint: Forces a decimal point and subsequent zeros on the output of an integer number input as a float. For the DevC++ compiler, both fixed and showpoint do this. You can use showpoint without the use of fixed and it will force a decimal ouput. If you use fixed, you do not need to use showpoint. 1. Syntax and Use: cout << showpoint ; Example of Use: float num1, num2 ; cout << showpoint ; cout << "Please enter two float numbers: " ; cin >> num1 >> num2; cout << endl; cout << num1 << " " << num2 << endl << endl; Page 14

15 Please enter two float numbers: What about using showpoint with the setprecision( ) manipulator? Example: float num1, num2 ; cout << showpoint << setprecision(2) ; cout << "Please enter two float numbers: " ; cin >> num1 >> num2; cout << endl; cout << num1 << " " << num2 << endl << endl; Please enter two float numbers: Another Example with setprecision(4) : Page 15

16 float num1, num2 ; cout << showpoint << setprecision(4) ; cout << "Please enter two float numbers: " ; cin >> num1 >> num2; cout << endl; cout << num1 << " " << num2 << endl << endl; Please enter two float numbers: Notice that showpoint with setprecision( ) controls all of numbers in the float, not just the digits after the decimal point. E. setw: Outputs the value of an expression in specified columns. The value of the expression can be a number, a character, or a string. How it works is that the statement setw(n) outputs the next expression in n columns and right justifies that expression in the n columns. If the number of columns specified is less than the number of columns required by the output, then the output is automagically expanded so as not to truncate the expression. NOTE: The setw( ) manipulator only works on the next expression output. It is not like the setprecision( ) or fixed manipulators that can be called once and all subsequent outputs will conform. 1. Syntax and Use: cout << setw( n ) << variable or expression ; Example of Use: Page 16

17 float num1, num2 ; cout << showpoint << setprecision(4) ; cout << "Please enter two float numbers: " ; cin >> num1 >> num2; cout << endl; cout << " " << endl; cout << setw(10) << num1 << setw(10) << num2; cout << endl << endl; Please enter two float numbers: Note that the setw( ) manipulator can be used without other manipulators or in conjunction with them. To use setw( ), you must also include the preprocessor directive: Another Example without Numbers: cout << setw(22) << "Alan Jay Spurgeon" << endl ; cout << setw(26) << "1313 Mockingbird Lane" << endl ; cout << setw(10) << "Eerie" << setw(4) << "IN" ; cout << setw(7) << "01313" << endl << endl; Page 17

18 Alan Jay Spurgeon 1313 Mockingbird Lane Eerie IN Another example with the setw( ) not wide enough for output. Notice that the setw(5) is smaller than the number of columns needed to output the string to the screen. Also notice that it does not chop off the string to the first 5 characters or the last 5 characters, but prints out the whole thing. Example: cout << setw(5) << "Alan Jay Spurgeon" << endl ; cout << setw(5) << "1313 Mockingbird Lane" << endl ; cout << setw(5) << "Eerie" << setw(4) << "IN" ; cout << setw(7) << "01313" << endl << endl; Alan Jay Spurgeon 1313 Mockingbird Lane Eerie IN V. Additional Output Formatting Tools A. fill and setfill: A function and manipulator that allows the programmer to fill the blank spaces caused by a setw( ) manipulator with a specified character. Page 18

19 1. Syntax and Use for fill: ostreamvar.fill ( ch ) ; i. Where ostreamvar would be cout if we are outputting to the screen. ii. iii. iv. Where ch would be some character data type variable or a character between single quotes. Like the manipulators fixed and setprecision( ), the fill function only has to be called once to affect the output afterwards until it is changed again by code. Example: cout.fill('*') ; cout << setw(22) << "Alan Jay Spurgeon" << endl ; cout << setw(26) << "1313 Mockingbird Lane" << endl ; cout << setw(10) << "Eerie" << setw(4) << "IN" ; cout << setw(7) << "01313" << endl << endl; *****Alan Jay Spurgeon *****1313 Mockingbird Lane *****Eerie**IN**01313 v. Another Example Page 19

20 cout.fill('*') ; cout << setw(22) << "Alan Jay Spurgeon" << endl ; cout << setw(26) << "1313 Mockingbird Lane" << endl ; cout.fill('#'); cout << setw(10) << "Eerie" << setw(4) << "IN" ; cout << setw(7) << "01313" << endl << endl; *****Alan Jay Spurgeon *****1313 Mockingbird Lane #####Eerie##IN## Syntax and Use of setfill: ostreamvar << setfill( ch ) ; i. Where ostreamvar would be cout if we are outputting to the screen. ii. iii. iv. Where ch would be some character data type variable or a character between single quotes. Like the manipulators fixed and setprecision( ), the setfill manipulator only has to be called once to affect the output afterwards until it is changed again by code. Example: cout << setfill('*') << setw(22) << "Alan Jay Spurgeon" << endl ; cout << setw(26) << "1313 Mockingbird Lane" << endl ; Page 20

21 cout << setw(10) << "Eerie" << setw(4) << "IN" ; cout << setw(7) << "01313" << endl << endl; *****Alan Jay Spurgeon *****1313 Mockingbird Lane *****Eerie**IN**01313 v. Another Example: cout << setfill('*') << setw(22) << "Alan Jay Spurgeon" << endl ; cout << setw(26) << "1313 Mockingbird Lane" << endl ; cout << setfill('^') << setw(10) << "Eerie" << setw(4) << "IN" ; cout << setw(7) << "01313" << endl << endl; *****Alan Jay Spurgeon *****1313 Mockingbird Lane ^^^^^Eerie^^IN^^ fill and setfill can be used interchangeably. Page 21

22 B. The left and right Manipulators: Allows the programmer to left or right justify when using the setw( ) manipulator. Recall that the default justification is right. 1. Syntax and Use: ostreamvar << left; i. Where ostreamvar would be cout since we have not changed the default output device. ii. The fill manipulator works like the fixed and setprecision( ) manipulators, once called, it is in effect until changed. iii. Example: cout << left << setw(22) << "Alan Jay Spurgeon" << endl ; cout << setw(26) << "1313 Mockingbird Lane" << endl ; cout << setw(10) << "Eerie" << setw(4) << "IN" ; cout << setw(7) << "01313" << endl << endl; Alan Jay Spurgeon 1313 Mockingbird Lane Eerie IN iv. Another Example: Page 22

23 cout << left << setw(22) << "Alan Jay Spurgeon" << endl ; cout << setw(26) << "1313 Mockingbird Lane" << endl ; cout << right << setw(10) << "Eerie" << setw(4) << "IN" ; cout << setw(7) << "01313" << endl << endl; Alan Jay Spurgeon 1313 Mockingbird Lane Eerie IN v. Another way to undo the call for left justification is the following: cout.unsetf ( ios :: left ) ; vi. Again, another way to do the same thing as cout << left << right. cout.setf ( ios :: left, ios :: adjustfield ) ; or cout.setf ( ios :: right, ios :: adjustfield ) ; or cout << setiosflags ( ios :: left ) ; C. The flush Function: Allows the programmer to force the output buffer to print to the screen even if it is not full. The endl function does the same thing except that it also forces a newline. When you do not want a new line, use the flush function. 1. Syntax and Use: ostreamvar.flush ( ) ; or ostreamvar << "some expression" << flush; i. Where ostreamvar is cout if the default output device has not been changed. Page 23

24 ii. Example: int num1, num2 ; cout << "Enter an integer: " ; cout.flush( ) ; cin >> num1 ; cout << "Enter another integer: " << flush ; cin >> num2 ; cout << num1 << setw( 8 ) << num2 << endl; cout << endl ; 2. Reminder: Enter an integer: 34 Enter another integer: i. To use the stream functions: get, ignore, fill, clear, and setf, you must include the header file iostream. ii. To use a stream manipulator with parameters such as: setprecision, setw, setfill, and setiosflags, you must include the header file iomanip. D. Input/Output and the string Type 1. You can save a string to a string variable type from the input device using Page 24

25 the cin >> ( inputstreamvariable and extraction operator ). Remember, though, that cin >> ignores white space!! 2. Example of use: #include <string> string firstname, lastname, name ; cout << "Enter your first name here: " ; cin >> firstname ; cout << "Enter your last name here: " ; cin >> lastname ; cout << "Your name is " << firstname << " " << lastname ; cout << endl << endl ; Enter your first name here: Alan Enter your last name here: Spurgeon Your name is Alan Spurgeon 3. You can not do this: Same code... Produces the following output with different input: Enter your first name here: Alan Spurgeon Enter your last name here: Your name is Alan Spurgeon Page 25

26 4. To read strings containing blanks you must use the getline function. This function will read all characters up to, but not including, a new line character. i. Syntax and Use: getline ( istreamvar, strvar ) ; a. Where istreamvar is cin unless the default input device has been changed. b. Where strvar is a variable that is declared of type string. Don't forget to include the header file string. c. Now let's look at the previous program using the getline function: #include <string> string name ; cout << "Enter your first and last name here: " ; getline( cin, name ); cout << "Your name is " << name ; cout << endl << endl ; Enter your first and last name here: Alan Spurgeon Your name is Alan Spurgeon ii. Remember that the getline function does not ignore blank spaces, so be careful you do not have blank spaces where you don't want them ( at the beginning or end especially ). Page 26

27 5. You may also output strings to the standard or default output device by using the cout << ( outputstream variable and insertion operator ) For an example, look at the previous code and output example. VI. File Input/Output A. Purpose: Not all data has to originate from the keyboard or be output to the screen. In cases where a large amount of data is to be input or output, it is more efficient to read in from or out to a file. 1. File: An area in secondary storage used to hold data. B. Procedure: Reading data in from a file or writing data out to a file is a five step process: 1. Include the header file fstream in the program 2. Declare file stream variables 3. Associate the file stream variables with the input/output sources 4. Use the file stream variables with >>, << or other input/output functions 5. Close the files C. More Detail: 1. Step 1: Make sure you put the statement #include <fstream> with the rest of the header files you are using. 2. Step 2 : Declare your file stream variables such as: ifstream infile ; input file stream variable like a data type for input stream variables ofstream outfile ; output file stream variable like a data type for output stream var.s Page 27

28 3. Step 3 : Open the File(s) by associating the file stream variables with the input/output sources. i. Syntax for opening a file: filestreamvariable.open ( sourcename, fileopeningmode ); a. Where filestreamvariable would be the identifier name you created, like infile or outfile in the example in Step 2. b. Where sourcename is the file path and file name of where you want data written from or to. Example: infile.open( "C : myfile.dat " ) ; Notice that the file path and name are enclosed in double quotes. Also, if you want to open a file that is in the same directory as your source code, you can eliminate the file path and just put the filename inside double quotes. Example: outfile.open ( "myfile.dat " ) ; c. Where fileopeningmode is a mode in which the file is to be opened. This is an optional part of the syntax that does not have to be included if you want the default mode. File-Opening Mode ios :: in ios :: out ios :: nocreate ios :: app ios :: ate Description Opens the file for input. This is the default for ifstream variables. Opens the file for output. This is the default for ofstream variables. If the file does not exist, the open operation fails. If the file exists, adds the output at the end of the file ( append ). If the file does not exist, creates an empty file. Opens the file for output and moves to the end of the file. Output may be written anywhere in the file. ios :: trunc If the file exists, the contents will be deleted ( truncated ). ios :: noreplace If the file exists, the open operation fails. Page 28

29 d. Examples of use : infile.open ( "mydata.dat", ios :: nocreate ) ; outfile.open ( "yourdata.dat", ios :: app ) ; infile.open ("A:School\myData.dat", ios :: nocreate); outfile.open ( "yourdata.dat", ios :: trunc ) ; 4. Step 4 : Use your file stream variables with <<, >>, or any other input/output functions. In other words, where ever you would normally use the cin or cout variables, you instead use the file stream variables you made up. i. Examples: Instead of : cout << "Hello World!" << endl; Write this : outfile << "Hello World!" << endl; Instead of : cin >> num1 >> num2 ; Write this : infile >> num1 >> num2; Instead of : cout << fixed << setprecision (2 ); Write this : outfile << fixed << setprecision (2 ); Instead of : getline ( cin, stringvar ) ; Write this : getline ( infile, stringvar ) ; Get the idea? 5. Step 5 : Close the file(s). i. Syntax and Use: filestreamvariable.close ( ); a. Where filestreamvariable is the variable name you created, such as infile, outfile, indata, outdata, etc. b. Example : Page 29

30 infile.close ( ) ; or outfile.close ( ) ; D. Example Program Using Input and Output file: #include <fstream> ifstream infile; ofstream outfile; int num1, num2 ; float avg ; infile.open( "mydata.dat", ios :: nocreate ); outfile.open ( "yourdata.dat", ios :: app ); infile >> num1 >> num2; avg = (num1 + num2) / 2.0 ; outfile << fixed << setprecision(2); outfile << "The average of the two numbers is: " << avg ; outfile << endl << endl ; infile.close( ); outfile.close ( ); V. Binary Conversion A. Binary to Decimal 1. Binary Notation (Method of representing numbers using only 1's and 0's) 2. Given the number 19 in the decimal system: Page 30

31 = ( 1 x 10 ) + ( 9 x 10 ) 3. Now we demonstrate the same number in the Binary System i. 19 (decimal) = (binary) ii = ( 1 x 2 ) + ( 0 x 2 ) + ( 0 x 2 ) + ( 1 x 2 ) + ( 1 x 2 ) 4. Now we demonstrate how to convert from binary to decimal. Given the binary number B. Decimal to Binary 0 = 1 * 2 = 1 1 = 1 * 2 = 2 2 = 0 * 2 = 0 3 = 1 * 2 = Given the decimal number / 2 = 33 with remainder of 1 33 / 2 = 16 with remainder of 1 16 / 2 = 8 with remainder of 0 8 / 2 = 4 with remainder of 0 4 / 2 = 2 with remainder of 0 2 / 2 = 1 with remainder of 0 1 Stop when you get a one ( 1 ) here. Now take the remainders in reverse order, starting with the bottom one. Therefore the answer is : = 67 Page 31