Boolean Features of Sign-Flipping and Signed-Carry Logic in Base -2

A direct self-contained proof of sign-flipping logic for base -2 binary numbers is derived and the same approach is extended to the derivation of a particular adder logic. Sign-flipping equations are contrasted with the logic for assimilated complement in classical binary. Logic equations for signed-carry addition and subtraction are then derived for various codes of interstage carry. Reduction of these operations to ordinary addition and subtraction logic, as well as reduction of base -2 subtraction to base -2 addition and use of Boolean complements is analyzed. Lastly, addition logic equations are derived for sign flipping as a special case of base -2 addition logic.