Figure 4

Example of naive summation based on a ripple carry adder. The A variables are used for storing the accumulation of the sum. The A^{1, t}variables, with 1 ≤ t ≤ 3, are constrained to zero. Additionally, the C^l,1and the B variables, except the B^l,1variables, with 1 ≤ l ≤ 4, are also constrained to zero. The S variables are set to the binary representation of the required sum, e.g. if S = (1, 0, 0), the only satisfying assignment of Boolean values to the B^l,1variables is (1, 1, 1, 1). If S = (0, 1, 0), there are six satisfying assignments to the B^l,1variables, namely (1, 1, 0, 0), (1, 0, 1, 0), (1, 0, 0, 1), (0, 1, 0, 1), (0, 0, 1, 1) and (0, 1, 1, 0).