Mirror arithmetic

Abstract

Mirror coding for signed numbers is defined "by means pf a set of primitive powers of two {+2ⁿ, −2ⁿ⁻¹, …−2°} where signs of the usual set used in 2's complement representation are reversed. Use of the mirror representation is shown as an alternate design approach and is illustrated "by a special purpose adder design in mirror code, by an alternate proof of a basic property of sign-ed-digit arithmetic and as another interpretation of cells used in some array multipliers for signed numbers. Lastly, the concept is used to define a variable mode redundant coding, allowing simple sign-flipping without overflow.