High Precision Carry-Look-Ahead Logic for Negation, Absolute Value, and Two’s Complement

This paper presents a novel paradigm, based on carry-look-ahead principles, for finding the negation of a high-precision binary integer represented in two’s complement, and also for converting a two’s complement number to sign-and-magnitude (i.e., absolute value), and vice versa. Theoretical analysis of the proposed algorithm yields a logarithmic bound on delay with increasing input size n. Implementation results of the proposed hardware show linear growth in complexity. The linear growth for lookup tables is also small: around 1.1n for the hardware alone and less than 2n for the hardware with a serial transceiver after n=512, due to overhead. Flip-flop usage grows similarly. The proposed hardware has a delay of 2.254 ns or less for all three aforementioned operations.