Logical right shift (${\mathrm{LSR}}_k(a)=\lfloor a/2^k\rfloor$)

A logical right shift moves bits toward less significant positions, discards those shifted out, and fills the high positions with zero. On the unsigned interpretation of a machine word, it computes the quotient in integer division by $2^k$. Indeed, splitting the binary representation after its lowest $k$ bits gives $a=2^{k}q+r$ with $0\le r<2^k$; the retained upper bits represent $q$. A fixed-width left bit shift by $n-k$ followed by a logical right shift by $n-k$ extracts precisely the low $k$ bits, giving the remainder.