211: Computer Architecture Summer 2016

Transcription

1 211: Computer Architecture Summer 2016 Liu Liu Topic: C Programming Data Representation

2 I/O: - (example) cprintf.c Memory: - memory address - stack / heap / constant space - basic data layout Pointer: - pointer type - declaration / initialization / assignment - pointer to an array - pointer in / de crement Dynamic Memory Allocation: - motivation - malloc() / free() - heap Call by value / reference: - array / array item / structure as parameters - (example) swap 2 vars Recap Rutgers University Liu Liu 2

3 Today s Topic - 1 more example on pointer - Project-1 related: - Command-line args - Parsing / realloc() - File I/O - String operations - C wrap up ************************************* Data representation********************************** - Data representation: - Numerical numbers in B / O / D / H - Endian / Complement - Floating number - Characters - Computer Arithmetic: - add / sub / mul / div (unsigned / signed) Rutgers University Liu Liu 3

4 When using a shell $ hello 5 Command Line Arguments Entire command line will be given to your program as a sequence of strings White spaces are typically the separator characters Shell dependent int main(int argc, char * argv []) { } argc: number of strings in command line» In our example, argc = 2 argv: the strings themselves» In our example, argv[0] = hello\0 and argv[1] = 5\0 Rutgers University Liu Liu 4

5 File I/O A file is a contiguous set of bytes Has a name Can create, remove, read, write, and append Unix/Linux supports persistent files stored on disk Access using system calls: open(), read(), write(), close(), creat(), lseek() Provide random access Section 2 of online manual (man) C supports extended interface to UNIX files fopen(), fscanf(), fprintf(), fgetc(), fputc(), fclose() View files as streams of bytes Section 3 of online manual (man) Rutgers University Liu Liu 5

6 fopen The fopen (pronounced "eff-open") function associates a physical file with a stream. FILE *fopen(char* name, char* mode); First argument: name The name of the physical file, or how to locate it on the storage device. This may be dependent on the underlying operating system. Second argument: mode How the file will be used: "r" -- read from the file "w" -- write, starting at the beginning of the file "a" -- write, starting at the end of the file (append) Rutgers University Liu Liu 6

7 fprintf and fscanf Once a file is opened, it can be read or written using fscanf() and fprintf() These are just like scanf() and printf() except with an additional argument specifying a file pointer fprintf(outfile, "The answer is %d\n", x); fscanf(infile, "%s %d/%d/%d %lf", &name, &bmonth, &bday, &byear, &gpa); When started, each executing program has three standard streams open for input, output, and errors stdin, stdout, stderr Rutgers University Liu Liu 7

8 Strings: Arrays of Characters Allocate space for a string just like any other array: char outputstring[16]; Each string should end with a \0 character Special syntax for initializing a string: char outputstring[16] = "Result"; which is the same as: outputstring[0] = 'R'; outputstring[1] = 'e';... outputstring[6] = \0 ; The \0 allows functions like strlen() to work on arbitrary strings Rutgers University Liu Liu 8

9 Useful functions for Strings Useful string related functions in standard C libraries #include <string.h> char *strcpy(char *d, char *s) Copy string s to d int strcmp(s1, s2) size_t strlen(s) Compare string s1 to s2 Returns length of cs Use man to learn more about these functions man strcpy Rutgers University Liu Liu 9

10 Special Character Literals Certain characters cannot be easily represented by a single keystroke, because they correspond to whitespace (newline, tab, backspace,...) are used as delimiters for other literals (quote, double quote,...) These are represented by the following sequences: \n newline \t tab \b backspace \\ backslash \' single quote \" double quote Rutgers University Liu Liu 10

11 realloc() The realloc (re-allocation) function dynamically changes the size of allocated space pointed by ptr to size. void *realloc(void* ptr, size_t size); First argument: ptr A pointer pointing to a pre-allocated space, or NULL; if ptr==null, realloc() == malloc() Second argument: size The new size of this memory space Function procedure: Copy the content of size = min(size, origin_size) free the old pointer malloc a new space with a new pointer returned(could be the same as old one) return the pointer if succeed, or NULL if not. Rutgers University Liu Liu 11

12 Data Representations Rutgers University Liu Liu 12

13 What Do Computer Do? Manipulate stored information Information is data How is it represented? Basic information: numbers Human beings have represented numbers throughout history Egyptian number system Discoveregypt.com Roman numeral Typically decimal Natural for humans Rutgers University Liu Liu 13

14 Comprises of Number System Set of numbers or elements Operations on them Rules that define properties of operations Need to assign value to numbers Let us take decimal Base 10 Numbers are written as d n...d 2 d 1 d 0 Each digit is in [0-9] Value of a number is interpreted as i= n 0 d i i 10 Rutgers University Liu Liu 14

15 Binary Numbers Base 2 each digit is 0 or 1 Numbers are written as d n...d 2 d 1 d 0 Value of number is computed as Binary representation is used in computers Easy to represent by switches (on/off) Manipulation by digital logic in hardware Written form is long and inconvenient to deal with n i= 0 d i 2 i Rutgers University Liu Liu 15

16 Hexadecimal Numbers Base 16 Each digit can be one of 16 different values Symbols = {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F} First 10 symbols (0 through 9) are same as decimal A=10,B=11,C=12, D=13, E=14, F=15 Numbers are written as d n...d 2 d 1 d 0 n Value = i= 0 d i 16 i Rutgers University Liu Liu 16

17 Base 8 each digit is in [0-7] Octal Numbers Numbers are written as d n...d 2 d 1 d 0 n Value of number is computed as i= 0 d i 8 i Rutgers University Liu Liu 17

18 Converting Hex to Binary Each hexadecimal digit can be represented by 4 binary digits Why? 0x2A8C (hex) = 0b (binary) 0xC = 12 x 16 0 = = (1 x 2 3 ) + (1 x 2 2 ) = 0b1100 0x80 = 8 x 16 1 = 2 3 x 2 4 = 2 7 = 0b And so on So, to convert hex to binary, just convert each digit and concatenate. What about octal to binary? Rutgers University Liu Liu 18

19 Converting Binary to Hex Do the reverse Group each set of 4 digits and change to corresponding digit in hex Go from right to left Example b = 0xB79C What if a binary number has 7 digits? What about binary to octal? Rutgers University Liu Liu 19

20 Decimal to Binary What s the largest p, q, r such that n = 2 p + r 1, where r 1 < 2 p n - 2 p = 2 q + r 2, where r 2 < 2 q n (2 p + 2 q )= 2 r + r 3, where r 3 < 2 r The above means that n = (1 x 2 p ) + (1 x 2 q ) + (1 x 2 r ) + + r m, where r m = n % 2 Can you see why this now allows n to be easily written in binary form? Example: convert 21 to binary 21 = , 5 = = 0b10101 Rutgers University Liu Liu 20

21 Decimal to Binary and Back How to do the conversion algorithmically? What about binary to decimal? What about decimal to hex? Hex to decimal? Decimal to octal? Octal to decimal? Hex to octal? Octal to Hex? Rutgers University Liu Liu 21

22 Decimal and Binary fractions In decimal, digits to the right of radix point have value 1/10 i for each digit in the i th place 0.25 is 2/10 + 5/100 Similarly, in binary, digits to the right of radix point have value 1/2 i for each i th place Just the base is different is = 6/10 + 2/ /1000 = 1/2 + 1/8 How to convert? Rutgers University Liu Liu 22

23 Decimal to Binary Example Algorithm Number = decimalfraction while (number > 0) { number = number*2 if (number >=1) { Output 1; number = number-1 } else { Output 0 } } Why does it work? Example: to binary ANS: *2 = 1.25 output *2 =0.5 output 0 0.5*2 = 1 output 1 Exit Rutgers University Liu Liu 23

24 Big Endian vs. Little Endian How to determine value when having a binary number spread across multiple bytes Is it A0BC0012 or 1200BCA0? One is called big endian and one is little endian Most Significant byte first big endian Lease significant byte first little endian Makes no difference to computer architecture Why do we care? A0 BC Interpret machine code and values One computer (big endian) sending data to another computer (little endian) Need to convert into standard form before transmitting Rutgers University Liu Liu 24

25 Representing integers How do we represent negative numbers in computers? Use a bit after all, that s how we store information, right? Signed Magnitude: S 0100 = 4, 1100 = -4 Magnitude 0011 = 3, 1011 = -3 What is 1000? Have two zeros +0 (0000) and -0 (1000) As we shall see, inconvenient for arithmetic computations Rutgers University Liu Liu 25

26 One s Complement Represent negative numbers by complementing positive numbers Still have two zeros but arithmetic computation becomes easier Rutgers University Liu Liu 26

27 Two s Complement One s complement plus one Most significant bit still gives the sign Trick: copy all 0 bits from LSB till first 1 bit. Copy 1 bit, then flip all remaining bits till MSB. Advantages: Only 1 zero Most convenient for arithmetic computations Used in almost all computers today Rutgers University Liu Liu 27

28 Numerical Value of Two s Complement Given a two s complement number of length n, written as d n-1 d 1 d 0 It s value is interpreted as n 2 n 1 i 12 + i 2 i= 0 d n d The range of values is then [ 2 1] More negative numbers than positive (if we do not count 0) 101 =? 0101!= 101,2 n 1 n 1 What about real numbers? Rutgers University Liu Liu 28

29 Floating point Integers typically written in ordinary decimal form E.g., 1, 10, 100, 1000, 10000, , etc. But, can also be written in scientific notation E.g., 1x10 4, x10 7 What about binary numbers? Works the same way 0b100 = 0b1x2 2 Scientific notation gives a natural way for thinking about floating point numbers 0.25 = 2.5x10-1 = 0b1x2-2 How to represent in computers? Rutgers University Liu Liu 29

30 IEEE floating point standard Most computers follow IEEE 754 standard Single precision (32 bits) Double precision (64 bits) Extended precision (80 bits) S Exponent Fraction Rutgers University Liu Liu 30

31 32 bits single precision (type float) Floating point in C 1 bit for sign, 8 bits for exponent, 23 bits for mantissa Sign bit: 1 = negative numbers, 0 = positive numbers Exponent is power of 2 Have 2 zero s Range is approximately to bits double precision (type double) 1 bit for sign, 11 bits for exponent, 52 bits for mantissa Majority of new bits for mantissa higher precision Range is to * *10+10, which one is has higher precision? Rutgers University Liu Liu 31

32 3 different cases: Numerical Values 1) Normalized values exponent field 0 and exponent field 2 k -1 (all 1 s) exponent = binary value Bias» Bias = 2 k-1-1 (e.g., 127 for float) mantissa = 1.(mantissa field) Ex: (sign: 0, exp: 1, mantissa: 1) would give 0b1.1x ) Denormalized values exponent field = 0 exponent = 1 Bias (e.g., -126 for float), why not -127? Mantissa = mantissa field (no leading 1) Ex: (sign: 0, exp: 0, mantissa: 10) would give 0b10x2-126 Rutgers University Liu Liu 32

33 Numerical Values 3 different cases: Special values: +, -, 0, and NaN what is the value of 32bit all 0? Is it 1.0*2-127? -> 0 +/- occurs when dividing a number with 0.0. What is 0.0 / 0.0? -> NaN(ill-defined value) Square root of a neg value? -> NaN Rutgers University Liu Liu 33

34 Numerical Values Rutgers University Liu Liu 34