A neural network apparatus that is configured to process an operation includes neural network circuitry configured to receive a first input of an n-bit activation, store a second input of an m-bit weight, perform a determination whether to perform an operation on an ith bit of the first input and a jth bit of the second input, output an operation value of an operation performed on the ith bit of the first input and the jth bit of the second input based on the determination, and produce an operation value of the operation based on the determination.