18bit wise operator to understand with -bits.ppt

18bit wise operator to understand with -bits.ppt

• 1.
  1 CSE 303 Lecture 18 Bitwiseoperations reading: Programming in C Ch. 12 slides created by Marty Stepp http://www.cs.washington.edu/303/
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  2 A puzzle... • Aking wishes to throw a grand party tomorrow in his castle. He has purchased 1000 bottles of wine to serve to his many guests. • However, a thief has been caught breaking into the wine cellar! He poisoned a single bottle. The poison is lethal at even the smallest dose; it causes death within approximately 12-15 hours.  The king wants to find out which bottle has been poisoned and throw it out so that his guests will not be harmed. • The king has over 1000 servants to help him, and a few dozen prisoners in his dungeon, but he does not want to risk servant lives if possible. The prisoners are vermin and may be sacrificed.  How should the king find the poisoned bottle? Hint: First solve it with 4 bottles of wine and 2 prisoners.
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  3 The answer • Numbereach bottle from 1 to 1000.  Convert the bottle numbers to ten-digit binary numbers, from 1 (00000001) to 1000 (1111101000). • Consider each of the 10 prisoners to represent one of the ten bits. • Each prisoner will drink from multiple bottles.  Prisoner i will drink every bottle for which bit i is 1. • The pattern of dead prisoners tells you which bottle was poisoned.  If prisoners 1, 3, and 7 die, bottle # (512 + 128 + 8) = 648 was bad. • moral : Tightly packed data can be a good thing to avoid waste.
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  4 Motivation • C wasdeveloped with systems programming in mind  lean, mean, fast, powerful, unsafe  pointers provide direct access to memory • C is often used in resource-constrained situations  devices without much memory  devices with slow processors  devices with slow network connections • it is sometimes necessary to manipulate individual bits of data  "twiddle with bits"  "bit packing"
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  5 Terms • bit: asingle binary digit, either 0 or 1 • nibble: 4 bits • byte: 8 bits (also sometimes called an "octet") • word: size of an integer on a given machine (often 32 bits) • hword: 16 bits ("half word") • dword: two words long ("double word", "long word")  How many unique values can be stored in a bit? A nibble? A byte?  How many unique values can be stored using N bits?
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  6 Bases, number systems •decimal (base-10) int x1 = 42;  most natural to humans • binary (base-2)  how the computer stores data • hexadecimal (base-16) int x2 = 0x2a;  memory addresses  each digit maps to 4 bits; concise • octal (base-8) int x3 = 052;  chmod permissions  each digit maps directly to 3 bits; no special number symbols used
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  7 Binary representations • recall:ints are stored as 32-bit (4-byte) integers int x = 42; int y = 1 + 128 + 256 + 4096 + 32768 + 131072; • the maximum positive int value that can be stored is 231 - 1 int z = 2147483647; 0000000 0 0000000 0 0000000 0 0010101 0 0000000 0 0000001 0 1001000 1 1000000 1 0111111 1 1111111 1 1111111 1 1111111 1
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  8 Negative binary numbers •left most bit is the "sign bit"; 0 for positive, 1 for negative  all 1s represents -1 ; subsequent negatives grow "downward" int x = -1; int y = -2, z = -3;  a single 1 followed by all zeros represents -(232 - 1) int z = -2147483648; // largest negative value 1111111 1 1111111 1 1111111 1 1111111 1 1000000 0 0000000 0 0000000 0 0000000 0 1111111 1 1111111 1 1111111 1 1111111 0 1111111 1 1111111 1 1111111 1 1111110 1
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  9 Negating in binary •negating a binary number  "ones complement" : flip the bits (wrong)  "twos complement" : flip the bits, add 1 (preferred) • converting a negative number from decimal to binary and back  add 1, then convert abs. value to binary, then flip bits  binary to decimal: flip bits, convert to decimal, subtract 1 int x = -27; // -27 + 1 = -26 // 26 2 = 11010 // flip = 00101 1111111 1 1111111 1 1111111 1 1110010 1
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  10 Bitwise operators  leftshift pads remaining right digits with 0  right shift pads w/ 0 or value of a's leftmost (most significant) bit  most operators can be used with =, such as &=, ~=, >>=  what is the difference between & and &&? ~ and ! ? expression description a & b AND ; all bits that are set to 1 in both a and b a | b OR ; all bits that are set to 1 in a or in b or both a ^ b XOR ; all bits that are set to 1 in a or in b but not in both ~a NOT ; the "ones complement" of the bits of a (all bits flipped) a << n LEFT SHIFT ; moves all digits to the left by n places; same as multiplying a * 2n a >> n RIGHT SHIFT ; moves all digits to the right by n places; same as dividing a / 2n
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  11 AND, OR, XOR,NOT 64 32 16 8 4 2 1 25 0 0 1 1 0 0 1 77 1 0 0 1 1 0 1 • What is 25 & 77 ? 0 0 0 1 0 0 1 • What is 25 | 77 ? 1 0 1 1 1 0 1 • What is 25 ^ 77 ? 1 0 1 0 1 0 0 • What is 25 & ~77 ? 0 0 1 0 0 0 0 bit1 bit2 bit1 & bit2 bit1 | bit2 bit1 ^ bit2 bit1 & ~bit2 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0
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  12 Bit shifting • Shiftingleft is like multiplying by powers of 2: int x = 42; // 101010 int y = x << 1; // 1010100 ( 84 = 42 * 2) int z = x << 3; // 101010000 (336 = 42 * 8) int w = x << 31; // 0 (why?) • Shifting right is like dividing by powers of 2: int x = 42; // 101010 int y = x >> 1; // 10101 (21) x = -42; // 111111...010110 int z = x >> 1; // 1111111...01011 (-21) • often faster than multiplication, but don't worry about that  "Premature optimization is the root of all evil." -- Donald Knuth
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  13 Exercises • Write functionsto do the following tasks:  print an integer in binary  rotate bits by n places  get/set a given bit from a given integer  get/set a given range of bits from a given integer  invert a given bit(s) of a given integer  Should these be functions or preprocessor macros?
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  14 Recall: integer types •integer types: char (1B), short (2B), int (4B), long (8B) • modifiers: short, long, signed, unsigned (non- negative) type bytes range of values printf char 1 0 to 255 %c octal %o hex %x short int 2 -32,768 to 32,767 %hi unsigned short int 2 0 to 65,535 %hu int 4 -2,147,483,648 to 2,147,483,647 %d, %i unsigned int 4 0 to 4,294,967,295 %u long long int 8 -9e18 to 9e18 - 1 %lli
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  15 Unsigned integers unsigned intx = 42u;  changes interpretation of meaning of bits; no negatives allowed  maximum is twice as high (leftmost bit not used to represent sign)  right-shift behavior not same (pads w/ 0 instead of sign bit)  seen in some libraries (size_t, malloc, etc.)  often used with bit-packing because we don't care about sign  why not use unsigned more often?  really, it's all just bits in the end...
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  16 Bit packing • bitpacking: storing multiple values in the same word of memory  example: storing a student's id, year, and exam score in a single int • boolean (bool) values could really be just 1 bit (0 or 1)  "bit flags"  but a bool is actually a 1-byte integer value (Why?) • integers known to be small could use fewer than 32 bits  example: student IDs, 7 digits (how many bits?)  example: homework/exam scores, up to 100 (how many bits?)
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  17 Bit flags #define REGISTERED0x1 #define FULLTIME 0x2 #define PAIDTUITION 0x4 #define ACADEMICPROBATION 0x8 #define HONORROLL 0x10 // 16 #define DEANSLIST 0x20 // 32 ... int student1 = 0; // set student to be registered and on honor roll student1 = student1 | REGISTERED | HONORROLL; // make sure student isn't on probation student1 = student1 & ~ACADEMICPROBATION;
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  18 Bit fields typedef structname { unsigned name : bitsWide; ... unsigned name : bitsWide; } name;  declares a field that occupies exactly bitsWide bits  can be declared only inside a struct  exact ordering of bits is compiler-dependent  can't make pointers to them; not directly addressable
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  19 Binary data I/O //writing binary data to a file int values[5] = {10, 20, 30, 40, 50}; FILE* f = fopen("saved.dat", "w"); fwrite(values, sizeof(int), 5, f); // reading binary data from a file int values[5]; FILE* f = fopen("saved.dat", "r"); fread(values, sizeof(int), 5, f); function description size_t fwrite(void* ptr, size_t size, size_t count, FILE* file) writes given number of elements from given array/buffer to file (size_t means unsigned int) size_t fread(void* ptr, size_t size, size_t count, FILE* file) reads given number of elements to given array/buffer from file