A left justification scale factor generator is described which is capable of scaling numbers for binary number groups off one, two, three and four bit groups. Two basic building block circuits are utilized in the scale factor generator's priority encoder, which looks at four binary bits and produces a two bit binary count that corresponds to the first non-zero input found, and an algebraic priority encoder which also receives a reference signal that allows it to indicate the significance of the priority detection level. By sensing correction factors at the first level of the system, the number of logic levels are kept to a minimum.