So I was asked to perform the simple task of doing a 3-bit arithmetic shift of the number 1101 (-3 in 2's complement notation). Now this is easy and it goes as 1101 -> 1110 -> 1111 -> 1111. So the final result should be 1111 (-1 in 2's complement notation).
However I also learned that shifting a number p=3 positions to the right is the same as dividing that number by 2^p=8. Therefore shouldn't my result be 0, since -3 dividing by 8 is 0 (with remainder -3). What am I missing in this apparent paradox?