How does the bitwise complement operator tilde work

Question

Why is it that  2 is equal to -3   How does   operator work

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First we have to split the given digit into its binary digits and then reverse it by adding at the last binary digit After this execution we have to give opposite sign to the previous digit that which we are finding the complent  2 -3 Explanation  2s binary  form is 00000010 changes to 11111101 this is ones complement  then complented 00000010 1 00000011 which is the binary form of three and with -sign I e -3

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I know the answer for this question is posted a long back  but I wanted to share my answer for the same   For finding the one   s complement of a number  first find its binary equivalent  Here  decimal number 2 is represented as 0000 0010 in binary form  Now taking its one   s complement by inverting  flipping all 1   s into 0   s and all 0   s into 1   s  all the digits of its binary representation  which will result in   0000 0010   1111 1101   This is the one   s complement of the decimal number 2  And since the first bit  i e   the sign bit is 1 in the binary number  it means that the sign is negative for the number it stored   here  the number referred to is not 2 but the one   s complement of 2    Now  since the numbers are stored as 2   s complement  taking the one   s complement of a number plus one   so to display this binary number  1111 1101  into decimal  first we need to find its 2   s complement  which will be   1111 1101   0000 0010   1   0000 0011   This is the 2   s complement  The decimal representation of the binary number  0000 0011  is 3  And  since the sign bit was one as mentioned above  so the resulting answer is -3   Hint  If you read this procedure carefully  then you would have observed that the result for the one   s complement operator is actually  the number  operand - on which this operator is applied  plus one with a negative sign  You can try this with other numbers too

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The bit-wise operator is a unary operator which works on sign and magnitude method as per my experience and knowledge    For example  2 would result in -3    This is because the bit-wise operator would first represent the number in sign and magnitude which is 0000 0010  8 bit operator  where the MSB is the sign bit   Then later it would take the negative number of 2 which is -2    -2 is represented as 1000 0010  8 bit operator  in sign and magnitude    Later it adds a 1 to the LSB  1000 0010   1  which gives you 1000 0011    Which is -3

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tl dr   flips the bits  As a result the sign changes   2 is a negative number  0b  101   To output a negative number ruby prints -  then two s complement of  2  -   2   1     - 2   1     3  Positive numbers are output as is   There s an internal value  and its string representation  For positive integers  they basically coincide   irb main  001 0 gt    i    2   gt   2  irb main  002 0 gt  2   gt  2   The latter being equivalent to   irb main  003 0 gt  2 to s  2      flips the bits of the internal value  2 is 0b010   2 is 0b  101  Two dots      represent an infinite number of 1 s  Since the most significant bit  MSB  of the result is 1  the result is a negative number    2  negative     true   To output a negative number ruby prints -  then two s complement of the internal value  Two s complement is calculated by flipping the bits  then adding 1  Two s complement of 0b  101 is 3  As such   irb main  005 0 gt    b    2   gt   10  irb main  006 0 gt    b     2   gt     101  irb main  007 0 gt   2   gt  -3   To sum it up  it flips the bits  which changes the sign  To output a negative number it prints -  then   2   1    2    2    The reason why ruby outputs negative numbers like so  is because it treats the stored value as a two s complement of the absolute value  In other words  what s stored is 0b  101  It s a negative number  and as such it s a two s complement of some value x  To find x  it does two s complement of 0b  101  Which is two s complement of two s complement of x  Which is x  e g    2   1    1    2    In case you apply   to a negative number  it just flips the bits  which nevertheless changes the sign    irb main  008 0 gt    b    -3   gt     101  irb main  009 0 gt    b     -3   gt   10  irb main  010 0 gt   -3   gt  2   What is more confusing is that  0xffffff00    0xff  or any other value with MSB equal to 1   Let s simplify it a bit   0xf0    0x0f  That s because it treats 0xf0 as a positive number  Which actually makes sense  So   0xf0    0x  f0f  The result is a negative number  Two s complement of 0x  f0f is 0xf1  So   irb main  011 0 gt    x     0xf0   gt     f0f  irb main  012 0 gt    0xf0  to s 16    gt   -f1    In case you re not going to apply bitwise operators to the result  you can consider   as a -x - 1 operator   irb main  018 0 gt  -2 - 1   gt  -3 irb main  019 0 gt  --3 - 1   gt  2   But that is arguably of not much use   An example Let s say you re given a 8-bit  for simplicity  netmask  and you want to calculate the number of 0 s  You can calculate them by flipping the bits and calling bit length  0x0f bit length    4   But  0xf0    0x  f0f  so we ve got to cut off the unneeded bits   irb main  014 0 gt    x      0xf0  amp  0xff    gt   f  irb main  015 0 gt    0xf0  amp  0xff  bit length   gt  4   Or you can use the XOR operator       irb main  016 0 gt  i   0xf0 irb main  017 0 gt    x    i     1  lt  lt  i bit length  - 1    gt   f

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Javascript tilde     coerces a given value to the one s complement--all bits are inverted   That s all tilde does  It s not sign opinionated  It neither adds nor subtracts any quantity    0 - gt  1 1 - gt  0    in every bit position  0   integer nbr of bits - 1    On standard desktop processors using high-level languages like JavaScript   BASE10 signed arithmetic is the most common  but keep in mind  it s not the only kind  Bits at the CPU level are subject to interpretation based on a number of factors  At the  code  level  in this case JavaScript  they are interpreted as a 32-bit signed integer by definition  let s leave floats out of this   Think of it as quantum  those 32-bits represent many possible values all at once  It depends entirely on the converting lens you view them through   JavaScript Tilde operation  1 s complement   BASE2 lens  0001 - gt  1110  - end result of   bitwise operation  BASE10 Signed lens  typical JS implementation   1  - gt  -2   BASE10 Unsigned lens   1  - gt  14    All of the above are true at the same time

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int a 4  System out println  a   Result would be  -5      of any integer in java represents 1 s complement of the no  for example i am taking  4 which means in binary representation 0100  first   length of an  integer is four bytes i e 4 8 8 bits for 1 byte  32  So in system memory 4 is represented as  0000 0000 0000 0000 0000 0000 0000 0100 now   operator will perform 1 s complement on the above binary no  i e 1111 1111 1111 1111 1111 1111 1111 1011- 1 s complement  the most significant bit represents sign of the no either - or    if it is 1 then sign is  -  if it is 0 then sign is     as per this our result is a negative number  in java the negative numbers are stored in 2 s complement form  the acquired result  we have to convert into 2 s complement  first perform 1 s complement  and just add 1 to 1 s complement   all the one will become zeros except most significant bit 1 which is our sign representation of the number that means for remaining 31 bits 1111 1111 1111 1111 1111 1111 1111 1011   acquired result of   operator  1000 0000 0000 0000 0000 0000 0000 0100   1 s complement                                         1    2 s complement   1000 0000 0000 0000 0000 0000 0000 0101 now the result is -5 check out this link for the video  lt  Bit wise operators in java  https   youtu be w4pJ4cGWe9Y

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Simply               As 2 s complement of any number we can calculate by inverting all 1s to 0 s and vice-versa than we add 1 to it     Here N   N produce results - N 1  always  Because system store data in form of 2 s complement which means it stores  N like this       N   -    N  1   - N 1      For example       N   10    1010   Than  N    0101   so    N    1010   so    N   1   1011    Now point is from where Minus comes  My opinion is suppose we have 32 bit register which means 2 31 -1 bit involved in operation and to rest one bit which change in earlier computation complement  stored as sign bit which is 1 usually  And we get result as  10   -11      -11   10      The above is true if printf   d   0    we get result   -1    But printf   u   0  than result  4294967295 on 32 bit machine

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This operation is a complement  not a negation   Consider that  0   -1  and work from there   The algorithm for negation is   complement  increment    Did you know   There is also  one s complement  where the inverse numbers are symmetrical  and it has both a 0 and a -0

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flips the bits in the value    Why  2 is -3 has to do with how numbers are represented bitwise  Numbers are represented as two s complement   So  2 is the binary value  00000010   And  2 flips the bits so the value is now   11111101   Which  is the binary representation of -3

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Remember that negative numbers are stored as the two s complement of the positive counterpart  As an example  here s the representation of -2 in two s complement   8 bits  1111 1110  The way you get this is by taking the binary representation of a number  taking its complement  inverting all the bits  and adding one  Two starts as 0000 0010  and by inverting the bits we get 1111 1101  Adding one gets us the result above  The first bit is the sign bit  implying a negative  So let s take a look at how we get  2   -3  Here s two again  0000 0010  Simply flip all the bits and we get  1111 1101  Well  what s -3 look like in two s complement  Start with positive 3  0000 0011  flip all the bits to 1111 1100  and add one to become negative value  -3   1111 1101  So if you simply invert the bits in 2  you get the two s complement representation of -3  The complement operator     JUST FLIPS BITS  It is up to the machine to interpret these bits

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It s easy  Before starting please remember that   1  Positive numbers are represented directly into the memory   2  Whereas  negative numbers are stored in the form of 2 s compliment   3  If MSB Most Significant bit  is 1 then the number is negative otherwise number is      positive   You are finding  2  Step 1 Represent 2 in a binary format         We will get  0000 0010  Step 2 Now we have to find  2 means 1 s compliment of 2                    1 s compliment               0000 0010                   gt  1111 1101          So   2     1111 1101  Here MSB Most significant Bit  is 1 means negative value   So          In memory it will be represented as 2 s compliment To find 2 s compliment first we         have to find 1 s compliment and then add 1 to it    Step3   Finding 2 s compliment of  2 i e 1111 1101                     1 s compliment                   Adding 1 to it         1111 1101                       gt  0000 0010                   gt  0000 0010                                                                               1                                                                       ---------                                                                       0000 0011          So  2 s compliment of 1111 1101  is 0000 0011    Step4   Converting back to decimal format                     binary format         0000 0011                gt  3                 In step2  we have seen that the number is negative number so the final answer would          be -3                                                                      So   2     -3

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I think for most people the confusion part comes from the difference between decimal number and signed binary number  so lets clarify it first   for human decimal world  01 means 1  -01 means -1  for computer s binary world  101 means 5 if it is unsigned  101 means  -4   1  if is signed while the signed digit is at position x    x  so 2 s flipped bit    2     010    101   -4   1   -3 the confusion comes from mixing up the signed result 101 -3  and the unsinged result 101 5

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here  2 in binary 8 bit  is 00000010 and its 1 s complement is 11111101  subtract 1 from that 1 s complement we get 11111101-1   11111100  here the sign is - as 8th character  from R to L  is 1 find 1 s complement of that no  i e  00000011   3 and the sign is negative that s why we get -3 here

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Basically action is a complement not a negation    Here x   x produce results - x 1  always    x    2  - 2 1   -3

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The Bitwise complement operator    is a unary operator   It works as per the following methods  First it converts the given decimal number to its corresponding binary value That is in case of 2 it first convert 2 to 0000 0010  to 8 bit binary number    Then it converts all the 1 in the number to 0 and all the zeros to 1 then the number will become 1111 1101   that is the 2 s complement representation of -3   In order to find the unsigned value using complement i e  simply to convert 1111 1101 to decimal   4294967293  we can simply use the  u during printing

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As others mentioned   just flipped bits  changes one to zero and zero to one  and since two s complement is used you get the result you saw   One thing to add is why two s complement is used  this is so that the operations on negative numbers will be the same as on positive numbers  Think of -3 as the number to which 3 should be added in order to get zero and you ll see that this number is 1101  remember that binary addition is just like elementary school  decimal  addition only you carry one when you get to two rather than 10    1101    0011    3       10000        0000    lose carry bit because integers have a constant number of bits    Therefore 1101 is -3  flip the bits you get 0010 which is two

[operators] How does the bitwise complement operator (~ tilde) work?

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