OUTLINE. Number system. Creating MATLAB variables Overwriting variable Error messages Making corrections Entering multiple statements per line

Transcription

1 1 LECTURE 2

2 OUTLINE Number system Integer number Decimal number Binary number Hexadecimal number Creating MATLAB variables Overwriting variable Error messages Making corrections Entering multiple statements per line 2

3 NUMBER SYSTEMS various data types available in MATLAB MATLAB recognizes several different kinds of numbers 3

4 INTEGER NUMBERS There are two distinct types Unsigned integers Signed integers use up to 64 bits to store integers Let s begin with a discussion of the base ten system for representing integers. Infinity and Not a Number >> 2/0 ans = Inf >> 0/0 ans = NaN 4

5 BASE TEN ( DECIMAL INTEGER ) Most of us are familiar with base ten arithmetic because that is the number system we have been using for all of our lives For example, the number 2345, when expanded in powers of ten, is written as follows. Then the rule is 2345 = = = t n 10 n + t n 1 10 n t t t

6 Indeed, we are free to use any base that we wish For example, we could use base seven. If we did, then the number (2316) 7 would be interpreted to mean (2316) 7 = This is easily expanded and written in base ten. (2316) 7 = = = 846 Therefore, the rule will be s n 7 n + s n 1 7 n s s s

7 MATLAB has a useful utility called base2dec for converting numbers in different bases to base ten. You can learn more about this utility by typing help base2dec at the MATLAB prompt. >> help base2dec BASE2DEC Convert base B string to decimal integer. BASE2DEC (S, B) converts the string number S of base B into its decimal (base 10) equivalent. B must be an integer between 2 and 36. S must represent a non-negative integer value. 7

8 Note/ Strings in MATLAB are delimited with single apostrophes. Therefore, if we wish to use this utility to change the base seven in the previous example (2316) 7 to base ten using MATLAB. we enter the following at the MATLAB prompt. >> base2dec( 2316,7) ans = 846 8

9 BINARY INTEGERS At the most basic level, the fundamental storage unit on a computer is called a bit. has two states 0 and 1 computers naturally use base two arithmetic. example, suppose that we have a byte of storage and the state of each bit is coded as The number ( ) 2 can be converted to base ten by the previous technique. ( ) 2 = = = 139 9

10 This is easily checked with MATLAB s base2dec utility. >> base2dec( ,2) ans = 139 However, since base two is commonly used when working with computers MATLAB has a special command for changing base two numbers into base ten numbers called bin2dec. >> help bin2dec BIN2DEC Convert binary string to decimal integer. X = BIN2DEC(B) interprets the binary string B and returns in X the equivalent decimal number. We can use bin2dec to check our conversion of ( ) 2 to a base ten number. >> bin2dec( ) ans =

11 In contrast, MATLAB provides a utility called dec2bin for changing base ten integers to base two. >> dec2bin(139) ans = Note that this agrees nicely with our previous result 11

12 HEXADECIMAL INTEGERS As the number of bits used to store integers increases, it becomes painful to deal with all the zeros and ones. For example, If we use 16 bits, most would find it challenging to correctly write a binary number such as ( ) 2 This number, when expanded in powers of 2, becomes

13 This can be rewritten as follows. ( ) ( ) ( ) ( ) This is equivalent to the following expression. 14 (2 4 ) (2 4 ) (2 4 ) (2 4 ) 0 Finally, we see that our number can be expanded in powers of

14 We need to make two points: Because we are expanding in base 16, the coefficients must be selected from the integers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15, as they are in the above expansion (the coefficients are 14, 2, 0 and 15). The coefficients 10, 11, 12, 13, 14, and 15 are not single digits. To take care of the second point, we make the following assignments: A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15. With these assignments, we can rewrite the expression E F 16 0 In practice, this is written in hexadecimal format as (E20F) 16 14

15 We can check our result using MATLAB utilities. First, use bin2dec to change ( ) 2 into decimal format. >> bin2dec( ) ans = Follow this with MATLAB s dec2hex command to find the hexadecimal representation. >> dec2hex(57871) ans = E20F 15

16 CREATING MATLAB VARIABLES MATLAB variables are created with an assignment statement. The syntax of variable assignment is variable name = a value (or an expression) For example, >> x = expression where expression is a combination of numerical values, mathematical operators, variables, and function calls. On other words, expression can involve: manual entry built-in functions user-defined functions 16

17 OVERWRITING VARIABLE Once a variable has been created, it can be reassigned if you do not wish to see the intermediate results you can put a semicolon at the end of the line >> t = 5; >> t = t+1 t = 6 17

18 ERROR MESSAGES If we enter an expression incorrectly MATLAB will return an error message. For example, in the following, we left out the multiplication sign *, in the following expression >> x = 10; >> 5x??? 5x Error: Unexpected MATLAB expression. 18

19 MAKING CORRECTIONS Of course correction can be made Don t try to retype the expression again A previously typed command can be recalled with the up-arrow key When the command is displayed at the command prompt, it can be modified 19

20 CONTROLLING THE HIERARCHY OF OPERATIONS OR PRECEDENCE For example, * 3 is different with (1 + 2) * 3 >> (1+2)*3 ans = 9 But try * 3 the result will be different >> 1+2*3 ans = 7 By adding parentheses, these two expressions give different results: 9 and 7 20

21 Operators are executed left to right using the following precedence Operation Symbol Precedence Parentheses ( ) Highest Power Division Multiplication ^ / * Addition or subtraction + or - Lowest Example/ (2*3)^2+6/3*4-(5-4)^3=?? 21

22 Controlling the appearance of floating point number MATLAB by default displays only 4 decimals in the result of the calculations for example by the default is format short command. >> format short >> x= However, we can show more decimal points by using format long command >> format long >> x= e

23 ENTERING MULTIPLE STATEMENTS PER LINE It is possible to enter multiple statements per line Use commas (,) or semicolons (;) to enter more than one statement at once. For example, >> a=7; b=cos(a), c=cosh(a) b = c =

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