Spintronic devices have in general demonstrated the feasibility of non-volatile memory storage and simple Boolean logic operations. Modern microprocessors have one further frequently used digital operation: bit-wise operations on multiple bits simultaneously. Such operations are important for binary multiplication and division and in efficient microprocessor architectures such as reduced instruction set computing (RISC). In this paper we show a four-stage vertical serial shift register made from RKKY coupled ultrathin (0.9 nm) perpendicularly magnetised layers into which a 3-bit data word is injected. The entire four stage shift register occupies a total length (thickness) of only 16 nm. We show how under the action of an externally applied magnetic field bits can be shifted together as a word and then manipulated individually, including being brought together to perform logic operations. This is one of the highest level demonstrations of logic operation ever performed on data in the magnetic state and brings closer the possibility of ultrahigh density all-magnetic microprocessors.