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

An arithmetic right shift propagates the sign bit into the vacated high positions. For a signed two's complement integer, its result is division by $2^k$ rounded down. This differs from C integer division on negative nonmultiples of $2^k$, because that quotient truncates towards zero. Shifting an $n$-bit word arithmetically by $n-1$ produces zero for a nonnegative value and the all-one word, representing $-1$, for a negative value.