The authors address the problem of computing the COMPARISON and ADDITION functions of two n-bit numbers using circuits of nonmonotone) MAJORITY gates. Given n Boolean variables as indicated, a nonmonotone MAJORITY gate is a Boolean function whose value is the given sign. We construct an explicit sparse polynomial whose sign computes the COMPARISON function of two integers. Similar polynomials are constructed for computing all the bits of the summation of the two integers. A crucial ingredient in our approach is the construction of a discrete version of a sparse ″delta polynomial″. WE construct sparse delta polynomials using generators matrices of certain linear block codes.