Arithmetic right shifting of bit vector

• Right shifting $x$ by $k$, fills the left end with $k$ repetitions of the most significant bit.
• Assuming a $w-$bit vector, $x=\left[x_{w-1},x_{w-2},\dots ,x_0\right]$, $x\gg k$ will give:
  • $\left[x_{w-1},\dots ,x_{w-1},x_{w-1},x_{w-2},\dots x_k\right]$
• Almost all machine instructions use arithmetic right shifts for signed data

Example

• $x=[1100]$
  • Here, MSB = 1
• $x>>2=[\text{11}\text{11}]$
  • The italicised 1s indicate the values that fill the left end

Another example

• $x=[0100]$
  • Here, MSB = 0
• $x>>2=[\text{00}\text{01}]$
  • The italicised 0s indicate the values that fill the left end

Sources

• Computer Systems - A Programmer’s Perspective

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