Odd behavior when Java converts int to byte

Question

int i  132   byte b   byte i  System out println b     Mindboggling  Why is the output -124

User · Answer

132 is outside the range of a byte which is -128 to 127  Byte MIN VALUE to Byte MAX VALUE  Instead the top bit of the 8-bit value is treated as the signed which indicates it is negative in this case  So the number is 132 - 256   -124

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Conceptually  repeated subtractions of 256 are made to your number  until it is in the range -128 to  127  So in your case  you start with 132  then end up with -124 in one step   Computationally  this corresponds to extracting the 8 least significant bits from your original number   And note that the most significant bit of these 8 becomes the sign bit    Note that in other languages this behaviour is not defined  e g  C and C

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132 in digits  base 10  is 1000 0100 in bits  base 2  and Java stores int in 32 bits   0000 0000 0000 0000 0000 0000 1000 0100  Algorithm for int-to-byte is left-truncate  Algorithm for System out println is two s-complement  Two s-complement is if leftmost bit is 1  interpret as negative one s-complement  invert bits  minus-one    Thus System out println int-to-byte     is    interpret-as  if-leftmost-bit-is-1  negative invert-bits minus-one   left-truncate 0000 0000 0000 0000 0000 0000 1000 0100           interpret-as  if-leftmost-bit-is-1  negative invert-bits minus-one   1000 0100          interpret-as negative invert-bits minus-one 1000 0100      interpret-as negative invert-bits 1000 0011     interpret-as negative 0111 1100    interpret-as negative 124    interpret-as -124   -124     nbsp  nbsp Tada

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N is input number case 1  0 lt  N lt  127  answer N  case 2  128 lt  N lt  256 answer N-256  case 3  N gt 256            temp1 N 256          temp2 N-temp 256          if temp2 lt  127   then answer temp2          else if temp2 gt  128  then answer temp2-256  case 4  negative  number input         do same procedure just change the sign of the solution

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In java int takes 4 bytes 4x8 32 bits byte   8 bits range -128 to  127  converting  int  into  byte  is like fitting big object into small box if sign in -ve takes 2 s complement example 1  let number be 130 step 1 130 interms of bits  1000 0010 step 2 condider 1st 7 bits and 8th bit is sign 1 -ve and   ve  step 3 convert 1st 7 bits to 2 s compliment             000 0010              -------------             111 1101        add         1           -------------             111 1110  126  step 4 8th bit is  quot 1 quot  hence the sign is -ve step 5 byte of 130 -126 Example2  let number be 500 step 1 500 interms of bits 0001 1111 0100 step 2 consider 1st 7 bits  111 0100 step 3  the remained bits are  11  gives -ve sign step 4  take 2 s compliment         111 0100       -------------         000 1011      add        1       -------------         000 1100  12  step 5 byte of 500 -12 example 3  number 300  300 1 0010 1100   1st 7 bits  010 1100   remaining bit is  0  sign   ve need not take 2 s compliment for  ve sign   hence 010 1100  44   byte 300   44

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Two s complement Equation       In Java  byte  N 8  and int  N 32  are represented by the 2s-complement shown above   From the equation  a7 is negative for byte but positive for int   coef    a7    a6  a5  a4  a3  a2  a1  a0 Binary  1     0   0   0   0   1   0   0 ---------------------------------------------- int     128   0   0   0   0   4   0   0    132 byte   -128   0   0   0   0   4   0   0   -124

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here is a very mechanical method without the distracting theories    Convert the number into binary representation  use a calculator ok   Only copy the rightmost 8 bits  LSB  and discard the rest  From the result of step 2  if the leftmost bit is 0  then use a calculator to convert the number to decimal  This is your answer  Else  if the leftmost bit is 1  your answer is negative  Leave all rightmost zeros and the first non-zero bit unchanged  And reversed the rest  that is  replace 1 s by 0 s and 0 s by 1 s  Then use a calculator to convert to decimal and append a negative sign to indicate the value is negative    This more practical method is in accordance to the much theoretical answers above  So  those still reading those Java books saying to use modulo  this is definitely wrong since the 4 steps I outlined above is definitely not a modulo operation

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A quick algorithm that simulates the way that it work is the following   public int toByte int number        int tmp   number  amp  0xff     return  tmp  amp  0x80     0   tmp   tmp - 256      How this work   Look to daixtr answer  A implementation of exact algorithm discribed in his answer is the following   public static int toByte int number        int tmp   number  amp  0xff      if   tmp  amp  0x80     0x80            int bit   1          int mask   0          for                   mask    bit              if   tmp  amp  bit     0                    bit  lt  lt  1                  continue                            int left   tmp  amp    mask               int right   tmp  amp  mask              left    left              left  amp     mask               tmp   left   right              tmp   - tmp  amp  0xff               break                      return tmp

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byte in Java is signed  so it has a range -2 7 to 2 7-1 - ie  -128 to 127  Since 132 is above 127  you end up wrapping around to 132-256 -124  That is  essentially 256  2 8  is added or subtracted until it falls into range   For more information  you may want to read up on two s complement

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often in books you will find the explanation of casting from int to byte as being performed by modulus division  this is not strictly correct as shown below what actually happens is the 24 most significant bits from the binary value of the int number are discarded leaving confusion if the remaining leftmost bit is set which designates the number as negative  public class castingsample   public static void main String args          int i      byte y      i   1024      for i   1024  i  gt  0  i--           y    byte i        System out print i     mod 128       i 128     also           System out println i     cast to byte             y

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If you want to understand this mathematically  like how this works  so basically numbers b w -128 to 127 will be written same as their decimal value  above that its  your number - 256    eg  132  the answer will be  132 - 256   - 124 i e    256   your answer in the number 256    -124  is 132  Another Example  double a   295 04  int b   300  byte c    byte  a  byte d    byte  b  System out println c         d     the Output will be 39 44   295 - 256    300 - 256   NOTE  it won t consider numbers after the decimal

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In Java  an int is 32 bits  A byte is 8 bits    Most primitive types in Java are signed  and byte  short  int  and long are encoded in two s complement    The char type is unsigned  and the concept of a sign is not applicable to boolean    In this number scheme the most significant bit specifies the sign of the number  If more bits are needed  the most significant bit   MSB   is simply copied to the new MSB   So if you have byte 255  11111111 and you want to represent it as an int  32 bits  you simply copy the 1 to the left 24 times   Now  one way to read a negative two s complement number is to start with the least significant bit  move left until you find the first 1  then invert every bit afterwards  The resulting number is the positive version of that number  For example  11111111 goes to 00000001   -1  This is what Java will display as the value   What you probably want to do is know the unsigned value of the byte   You can accomplish this with a bitmask that deletes everything but the least significant 8 bits   0xff   So   byte signedByte   -1  int unsignedByte   signedByte  amp   0xff    System out println  Signed      signedByte     Unsigned      unsignedByte     Would print out   Signed  -1 Unsigned  255   What s actually happening here    We are using bitwise AND to mask all of the extraneous sign bits  the 1 s to the left of the least significant 8 bits   When an int is converted into a byte  Java chops-off the left-most 24 bits  1111111111111111111111111010101  amp  0000000000000000000000001111111   0000000000000000000000001010101   Since the 32nd bit is now the sign bit instead of the 8th bit  and we set the sign bit to 0 which is positive   the original 8 bits from the byte are read by Java as a positive value

[java] Odd behavior when Java converts int to byte?

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