Operators and Assignments - Shift Operators

• << left-shift, >> right-shift, >>> unsigned right-shift
• only used on integer values
• binary numeric promotion is not performed on the operands; instead unary promotion is performed on each operand separately (JLS §15.19)
• both operands are individually promoted to int if their type is byte, short or char
• a long shift operator does not force a left-hand int value promotion to long (JLS§5.6.1)
• left-associative
• left-hand operator represents the number to be shifted
• right-hand operator specifies the shift distance

      value << 2      // 2 is the distance to be shifted
  

• when the value to be shifted (left-operand) is an int, only the last 5 digits of the right-hand operand are used to perform the shift. The actual size of the shift is the value of the right-hand operand masked by 31 (0x1f). ie the shift distance is always between 0 and 31 (if shift value is > 32 shift is 32%value)

35             00000000 00000000 00000000 00100011
31 -> 0x1f     00000000 00000000 00000000 00011111
&              -----------------------------------
Shift value    00000000 00000000 00000000 00000011   -> 3

-29            11111111 11111111 11111111 11100011
31 -> 0x1f     00000000 00000000 00000000 00011111
&              -----------------------------------
Shift value    00000000 00000000 00000000 00000011   -> 3

• when the value to be shifted (left-operand) is a long, only the last 6 digits of the right-hand operand are used to perform the shift. The actual size of the shift is the value of the right-hand operand masked by 63 (0x3D) ie the shift distance is always between 0 and 63 (if shift value is greater than 64 shift is 64%value)
• the shift occurs at runtime on a bit-by-bit basis

Left-shift << (JLS §15.19)

• bits are shifted to the left based on the value of the right-operand
• new right hand bits are zero filled
• equivalent to left-operand times two to the power of the right-operand
  For example, 16 << 5 = 16 * 2⁵ = 512

Decimal 16            00000000000000000000000000010000

Left-shift 5     00000000000000000000000000010000     
  fill right     0000000000000000000000000001000000000
  discard left        00000000000000000000001000000000 

• the sign-bit is shifted to the left as well, so it can be dropped off or a different sign can replace it

Right-shift >> (JLS §15.19)

• bits are shifted to the right based on value of right-operand
• new left hand bits are filled with the value of the left-operand high-order bit therefore the sign of the left-hand operator is always retained
• for non-negative integers, a right-shift is equivalent to dividing the left-hand operator by two to the power of the right-hand operator
  For example: 16 >> 2 = 16 / 2² = 4

Decimal 16       00000000000000000000000000010000

Right-shift 2      00000000000000000000000000010000  
  fill left      00000000000000000000000000000100  
  discard right  00000000000000000000000000000100  -> Decimal 4
  
Decimal -16      11111111111111111111111111110000

Right-shift 2      11111111111111111111111111110000
  fill left      1111111111111111111111111111110000
  discard right  11111111111111111111111111111100  -> Decimal -4

Unsigned right-shift >>> (JLS §15.19)

• identical to the right-shift operator only the left-bits are zero filled
• because the left-operand high-order bit is not retained, the sign value can change
• if the left-hand operand is positive, the result is the same as a right-shift
• if the left-hand operand is negative, the result is equivalent to the left-hand operand right-shifted by the number indicated by the right-hand operand plus two left-shifted by the inverted value of the right-hand operand
  For example: -16 >>> 2 = (-16 >> 2 ) + ( 2 << ~2 ) = 1,073,741,820

Decimal 16       00000000000000000000000000010000

Right-shift 2      00000000000000000000000000010000  
  fill left      00000000000000000000000000000100  
  discard right  00000000000000000000000000000100  -> Decimal 4

Decimal -16      11111111111111111111111111110000

>>> 2              11111111111111111111111111110000
  fill left      0011111111111111111111111111110000
  discard right  00111111111111111111111111111100  

Don't panic that it will take you forever to convert a shift question on the exam. You probably won't get more than one or two questions and they'll likely involve numbers under 20.

Also see

• Working with Binary, Hex, and Octal numbers

Example Code

• TestShift.java