Abstract: A 3x adder for adding 2a to a, where a is a binary number, the binary numbers 2a and a partitioned so that 2a=(xk . . . x0) and a=(yk . . . y0)where xi and yi have the same size for each i=0, 1, . . . , k, where the 3x adder provides the group generate terms for the sums xi+yi, i=0, 1, . . . , k, according to Boolean expressions, where for any sum xi+yi where xi and yi each have size n1+1, the number of Boolean variables in the product terms in the Boolean expression for the group generate terms of xi+yi do not exceed j+1, where j is the largest integer not exceeding ni/2.