It is shown that in a residue system with only the two moduli m-1 and m+1, base extension to modulus m is possible with savings in time and sometimes in hardware over conventional techniques. It is also shown that the underlying theory generalizes to provide comparable savings when extending any system with two moduli nm-1 and nm+1 (where n may be any integer) to include the third modulus m. For systems with more than two moduli, the savings are obtained in sign detection and partial base-extension operations. Savings are also possible during other residue operations (e.g., scaling, magnitude comparison, and overflow determination) in which sign detection and base extension are used.