Direct exchange interaction allows spins to be magnetically ordered. Additionally, it can be an efficient manipulation pathway for low-powered spintronic logic devices. We present a novel logic scheme driven by exchange between two distinct regions in a composite magnetic layer containing a bistable canted magnetization configuration. By applying a magnetic field pulse to the input region, the magnetization state is propagated to the output via spin-to-spin interaction in which the output state is given by the magnetization orientation of the output region. The dependence of this scheme with input field conditions is extensively studied through a wide range of micromagnetic simulations. These results allow different logic operating modes to be extracted from the simulation results, and majority logic is successfully demonstrated.