Bitwise operation and usage

Question

Consider this code   x   1          0001 x  lt  lt  2         Shift left 2 bits  0100   Result  4  x   2          Bitwise OR  0011   Result  3  x  amp  1          Bitwise AND  0001   Result  1   I can understand the arithmetic operators in Python  and other languages   but I never understood  bitwise  operators quite well  In the above example  from a Python book   I understand the left-shift but not the other two   Also  what are bitwise operators actually used for  I d appreciate some examples

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This example will show you the operations for all four 2 bit values:

10 | 12

1010 #decimal 10
1100 #decimal 12

1110 #result = 14

10 & 12

1010 #decimal 10
1100 #decimal 12

1000 #result = 8

Here is one example of usage:

x = raw_input('Enter a number:')
print 'x is %s.' % ('even', 'odd')[x&1]

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I think that the second part of the question        Also  what are bitwise operators actually used for  I d appreciate some examples    Has been only partially addressed  These are my two cents on that matter    Bitwise operations in programming languages play a fundamental role when dealing with a lot of applications  Almost all low-level computing must be done using this kind of operations    In all applications that need to send data between two nodes  such as    computer networks  telecommunication applications  cellular phones  satellite communications  etc     In the lower level layer of communication  the data is usually sent in what is called frames  Frames are just strings of bytes that are sent through a physical channel  This frames usually contain the actual data plus some other fields  coded in bytes  that are part of what is called the header  The header usually contains bytes that encode some information related to the status of the communication  e g  with flags  bits    frame counters  correction and error detection codes  etc  To get the transmitted data in a frame  and to build the frames to send data  you will need for sure bitwise operations   In general  when dealing with that kind of applications  an API is available so you don t have to deal with all those details  For example  all modern programming languages provide libraries for socket connections  so you don t actually need to build the TCP IP communication frames  But think about the good people that programmed those APIs for you  they had to deal with frame construction for sure  using all kinds of bitwise operations to go back and forth from the low-level to the higher-level communication   As a concrete example  imagine some one gives you a file that contains raw data that was captured directly by telecommunication hardware  In this case  in order to find the frames   you will need to read the raw bytes in the file and try to find some kind of synchronization words  by scanning the data bit by bit  After identifying the synchronization words  you will need to get the actual frames  and SHIFT them if necessary  and that is just the start of the story  to get the actual data that is being transmitted   Another very different low level family of application is when you need to control hardware using some  kind of ancient  ports  such as parallel and serial ports  This ports are controlled by setting some bytes  and each bit of that bytes has a specific meaning  in terms of instructions  for that port  see for instance http   en wikipedia org wiki Parallel port   If you want to build software that does something with that hardware you will need bitwise operations to translate the instructions you want to execute to the bytes that the port understand   For example  if you have some physical buttons connected to the parallel port to control some other device  this is a line of code that you can find in the soft application    read     read   0x80   gt  gt  4   amp  0x0f     Hope this contributes

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Think of 0 as false and 1 as true   Then bitwise and  amp   and or    work just like regular and and or except they do all of the bits in the value at once   Typically you will see them used for flags if you have 30 options that can be set  say as draw styles on a window  you don t want to have to pass in 30 separate boolean values to set or unset each one so you use   to combine options into a single value and then you use  amp  to check if each option is set   This style of flag passing is heavily used by OpenGL   Since each bit is a separate flag you get flag values on powers of two aka numbers that have only one bit set  1 2 0  2 2 1  4 2 2  8 2 3  the power of two tells you which bit is set if the flag is on   Also note 2   10 so x 2 is 110 6  not 111 7  If none of the bits overlap which is true in this case    acts like addition

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Bit representations of integers are often used in scientific computing to represent arrays of true-false information because a bitwise operation is much faster than iterating through an array of booleans   Higher level languages may use the idea of a bit array    A nice and fairly simple example of this is the general solution to the game of Nim  Take a look at the Python code on the Wikipedia page  It makes heavy use of bitwise exclusive or

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One typical usage     is used to set a certain bit to 1   amp  is used to test or clear a certain bit    Set a bit  where n is the bit number  and 0 is the least significant bit    unsigned char a     1  lt  lt  n   Clear a bit   unsigned char b  amp     1  lt  lt  n   Toggle a bit   unsigned char c     1  lt  lt  n   Test a bit   unsigned char e   d  amp   1  lt  lt  n      Take the case of your list for example   x   2 is used to set bit 1 of x to 1   x  amp  1 is used to test if bit 0 of x is 1 or 0

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There may be a better way to find where an array element is between two values  but as this example shows  the  amp  works here  whereas and does not   import numpy as np a np array  1 2  2 3  3 4   np where  a gt 2  and  a lt 3          Result  Value Error np where  a gt 2   amp   a lt 3    Result   array  1

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what are bitwise operators actually used for  I d appreciate some examples    One of the most common uses of bitwise operations is for parsing hexadecimal colours   For example  here s a Python function that accepts a String like  FF09BE and returns a tuple of its Red  Green and Blue values   def hexToRgb value         Convert string to hexadecimal number  base 16      num    int value lstrip       16          Shift 16 bits to the right  and then binary AND to obtain 8 bits representing red     r     num  gt  gt  16   amp  0xFF         Shift 8 bits to the right  and then binary AND to obtain 8 bits representing green     g     num  gt  gt  8   amp  0xFF         Simply binary AND to obtain 8 bits representing blue     b    num  amp  0xFF      return  r  g  b    I know that there are more efficient ways to acheive this  but I believe that this is a really concise example illustrating both shifts and bitwise boolean operations

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Bitwise operators are operators that work on multi-bit values  but conceptually one bit at a time    AND is 1 only if both of its inputs are 1  otherwise it s 0  OR is 1 if one or both of its inputs are 1  otherwise it s 0  XOR is 1 only if exactly one of its inputs are 1  otherwise it s 0  NOT is 1 only if its input is 0  otherwise it s 0    These can often be best shown as truth tables   Input possibilities are on the top and left  the resultant bit is one of the four  two in the case of NOT since it only has one input  values shown at the intersection of the inputs   AND   0 1     OR   0 1     XOR   0 1    NOT   0 1 ---- -----    --- ----     ---- ----    ---- ----  0    0 0      0   0 1       0   0 1          1 0  1    0 1      1   1 1       1   1 0   One example is if you only want the lower 4 bits of an integer  you AND it with 15  binary 1111  so       201  1100 1001 AND  15  0000 1111 ------------------  IS   9  0000 1001   The zero bits in 15 in that case effectively act as a filter  forcing the bits in the result to be zero as well   In addition   gt  gt  and  lt  lt  are often included as bitwise operators  and they  shift  a value respectively right and left by a certain number of bits  throwing away bits that roll of the end you re shifting towards  and feeding in zero bits at the other end   So  for example   1001 0101  gt  gt  2 gives 0010 0101 1111 1111  lt  lt  4 gives 1111 0000   Note that the left shift in Python is unusual in that it s not using a fixed width where bits are discarded - while many languages use a fixed width based on the data type  Python simply expands the width to cater for extra bits  In order to get the discarding behaviour in Python  you can follow a left shift with a bitwise and such as in an 8-bit value shifting left four bits   bits8    bits8  lt  lt  4   amp  255   With that in mind  another example of bitwise operators is if you have two 4-bit values that you want to pack into an 8-bit one  you can use all three of your operators  left-shift  and and or    packed val     val1  amp  15   lt  lt  4     val2  amp  15     The  amp  15 operation will make sure that both values only have the lower 4 bits  The  lt  lt  4 is a 4-bit shift left to move val1 into the top 4 bits of an 8-bit value  The   simply combines these two together    If val1 is 7 and val2 is 4                   val1            val2                                        amp  15  and    xxxx-0111       xxxx-0100   amp  15   lt  lt  4  left   0111-0000                                                                    ------- -------                                 or                 0111-0100

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To flip bits  i e  1 s complement invert  you can do the following   Since value ExORed with all 1s results into inversion   for a given bit width you can use ExOR to invert them   In Binary a 1010 -- gt  this is 0xA or decimal 10 then  c   1111   a   0101 -- gt  this is 0xF or decimal 15 ----------------- In Python a 10 b 15 c   a   b -- gt  0101 print bin c     gives  0b101

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Another common use-case is manipulating testing file permissions   See the Python stat module  http   docs python org library stat html   For example  to compare a file s permissions to a desired permission set  you could do something like   import os import stat   Get the actual mode of a file mode   os stat  file txt   st mode   File should be a regular file  readable and writable by its owner  Each permission value has a single  on  bit   Use bitwise or to combine   them  desired mode   stat S IFREG stat S IRUSR stat S IWUSR   check for exact match  mode    desired mode  check for at least one bit matching  bool mode  amp  desired mode   check for at least one bit  on  in one  and not in the other  bool mode   desired mode   check that all bits from desired mode are set in mode  but I don t care about    other bits  not bool  mode desired mode  amp desired mode    I cast the results as booleans  because I only care about the truth or falsehood  but it would be a worthwhile exercise to print out the bin   values for each one

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the following bitwise operators   amp         and   return values  based on their input  in the same way logic gates affect signals  You could use them to emulate circuits

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Whilst manipulating bits of an integer is useful  often for network protocols  which may be specified down to the bit  one can require manipulation of longer byte sequences  which aren t easily converted into one integer   In this case it is useful to employ the bitstring library which allows for bitwise operations on data - e g  one can import the string  ABCDEFGHIJKLMNOPQ  as a string or as hex and bit shift it  or perform other bitwise operations     gt  gt  gt  import bitstring  gt  gt  gt  bitstring BitArray bytes  ABCDEFGHIJKLMNOPQ    lt  lt  4 BitArray  0x142434445464748494a4b4c4d4e4f50510    gt  gt  gt  bitstring BitArray hex  0x4142434445464748494a4b4c4d4e4f5051    lt  lt  4 BitArray  0x142434445464748494a4b4c4d4e4f50510

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I hope this clarifies those two   x   2  0001   x 0010   2  0011   result   3     x  amp  1  0001   x 0001   1  0001   result   1

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I didn t see it mentioned above but you will also see some people use left and right shift for  arithmetic operations   A left shift by x is equivalent to multiplying by 2 x  as long as it doesn t overflow  and a right shift is equivalent to dividing by 2 x   Recently I ve seen people using x  lt  lt  1 and x    1 for doubling and halving  although I m not sure if they are just trying to be clever or if there really is a distinct advantage over the normal operators

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i didnt see it mentioned  This example will show you the  -  decimal operation for 2 bit values  A-B  only if A contains B   this operation is needed when we hold an verb in our program that represent bits  sometimes we need to add bits  like above  and sometimes we need to remove bits  if the verb contains then   111  decimal 7 - 100  decimal 4 -------------- 011  decimal 3   with python  7  amp   4   3   remove from 7 the bits that represent 4   001  decimal 1 - 100  decimal 4 -------------- 001  decimal 1   with python  1  amp   4   1   remove from 1 the bits that represent 4 - in this case 1 is not  contains  4

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Sets  Sets can be combined using mathematical operations    The union operator   combines two sets to form a new one containing items in either   The intersection operator  amp  gets items only in both   The difference operator - gets items in the first set but not in the second   The symmetric difference operator   gets items in either set  but not both    Try It Yourself   first    1  2  3  4  5  6  second    4  5  6  7  8  9   print first   second   print first  amp  second   print first - second   print second - first   print first   second    Result    1  2  3  4  5  6  7  8  9    4  5  6    1  2  3    8  9  7    1  2  3  7  8  9

[python] Bitwise operation and usage

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