Bit Representation

Q1.整数的表示

• most significant bit(the leftmost bit)

最高位是符号位。(There is no unsigned type in Java < 7)

• 原码 补码 反码

    0: 00000000 00000000 00000000 00000000
    5: 00000000 00000000 00000000 00000101
    -5:
       10000000 00000000 00000000 00000101
       11111111 11111111 11111111 11111010（取反)-> 反码
       11111111 11111111 11111111 11111011（+1) -> 补码
  

  Integer.MAX_VALUE + 1 = Integer.MIN_VALUE

  Integer.MIN_VALUE - 1 = Integer.MAX_VALUE

• Why 补码？

1.方便加法器容易扩展到正负数的加减法。

2.反码需要表示正负零，补码系统可多表示$$-2^(n-1)$$

Q2. ">>>" vs. ">>"

• signed shift ">>" - arithmetical 算数右移

    1111 1000 -8 >> 1 (对于负数来说也相当于除以2，不过是向下取整)
    1111 1100 -4 >> 1
    1111 1110 -2 >> 1
    1111 1111 -1
  

• unsigned shift ">>>" - logical 逻辑右移

Note: These is no "unsigned int" in Java!

    Two View of a int:
    1. 32 Bits, each of which is either 0 or 1
    2. arithmetic number