Design Methods for Digital Systems
Design Methods for Digital Systems
Subtraction by Minuend Complementation
IEEE Transactions on Computers
Arithmetic Algorithms in a Negative Base
IEEE Transactions on Computers
Fast Hardware Fourier Transformation Through Counting
IEEE Transactions on Computers
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A direct self-contained proof of sign-flipping logic for base -2 binary numbers is derived and the same approach is ex. tended 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.