A processor includes packed data registers, a decode unit, and an execution unit. The decode unit is to decode a four-dimensional (4D) Morton coordinate conversion instruction. The 4D Morton coordinate conversion instruction is to indicate a source packed data operand that is to include a plurality of 4D Morton coordinates, and is to indicate one or more destination storage locations. The execution unit is coupled with the packed data registers and the decode unit. The execution unit, in response to the decode unit decoding the 4D Morton coordinate conversion instruction, is to store one or more result packed data operands in the one or more destination storage locations. The one or more result packed data operands are to include a plurality of sets of four 4D coordinates. Each of the sets of the four 4D coordinates is to correspond to a different one of the 4D Morton coordinates.