Abstract: In a floating-point addition (and/or subtraction) of two normalized numbers where a normalized result is also desired, a generation of a carry (overflow) or a borrow from the most significant bit of a minuend operation will cause the resultant mantissa not to be normalized. A dual adder scheme is used to always provide a normalized result. One adder provides an unshifted result while the second adder provides a shifted result. A logic circuit looks for a carry out when performing addition and a bit value of the msb when performing subtraction to select the output from the adder providing the proper normalization. Rounding logic circuitry is used to predict the rounding of the resultant mantissa and carry bits are coupled as a carry-in to the adders to achieve the proper rounding in the same clock cycle as the adding/subtracting of the two mantissas.

Abstract: In a floating-point subtraction of two numbers where a normalized result is needed, a prenormalization circuit predicts the number of leading zeroes which will appear in the resultant mantissa, due to the close value of the two source operands. The prenormalization circuit then causes appropriate left shifts of the two operand mantissas prior to the subtraction (two's complement addition) is performed, wherein the resultant mantissa will already be normalized.