A circuit for performing energy-efficient and high-throughput multiply-accumulate (MAC) arithmetic dot-product operations and convolution computations includes a two dimensional crossbar array comprising a plurality of row inputs and at least one column having a plurality of column circuits, wherein each column circuit is coupled to a respective row input. Each respective column circuit includes an excitatory memristor neuron circuit having an input coupled to a respective row input, a first synapse circuit coupled to an output of the excitatory memristor neuron circuit, the first synapse circuit having a first output, an inhibitory memristor neuron circuit having an input coupled to the respective row input, and a second synapse circuit coupled to an output of the inhibitory memristor neuron circuit, the second synapse circuit having a second output. An output memristor neuron circuit is coupled to the first output and second output of each column circuit and has an output.