Graphene revealed a number of unique properties beneficial for electronics. However, graphene does not have an energy band-gap, which presents a serious hurdle for its applications in digital logic gates. The efforts to induce a band-gap in graphene via quantum confinement or surface functionalization have not resulted in a breakthrough. Here we show that the negative differential resistance experimentally observed in graphene field-effect transistors of "conventional" design allows for

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... tion of viable non-Boolean computational architectures with the gap-less graphene. The negative differential resistance - observed under certain biasing schemes - is an intrinsic property of graphene resulting from its symmetric band structure. Our atomistic modeling shows that the negative differential resistance appears not only in the drift-diffusion regime but also in the ballistic regime at the nanometer-scale - although the physics changes. The obtained results present a conceptual change in graphene research and indicate an alternative route for graphene's applications in information processing.