An embedded systems programmer needs to optimize a division routine. Instead of using a standard division instruction, they perform a logical shift right by k k\,k places on an NNN-bit register holding an unsigned binary integer XXX (where k<Nk < Nk<N). Which of the following expressions mathematically represents the value of the register after this operation?
⌈X×2−k⌉\lceil X \times 2^{-k} \rceil⌈X×2−k⌉
X×2kX \times 2^kX×2k
⌊X×2−k⌋\lfloor X \times 2^{-k} \rfloor⌊X×2−k⌋
⌊X÷2k⌋\lfloor X \div 2k \rfloor⌊X÷2k⌋