Methods and apparatuses relating to vector operations with operand base system conversion and re-conversion are described. In one embodiment, a method includes executing a single instruction by receiving a vector element of a first input vector and a vector element of a second input vector expressed in a first base system, converting the vector elements into a second lower base system to form a converted vector element of the first input vector and a converted vector element of the second input vector, performing an operation on the converted vector element of the first input vector and the converted vector element of the second input vector to form a result, accumulating in a register a portion of the result with a portion of a result of a prior operation expressed in the second lower base system, and converting contents of the register into the first base system.