A neural network (NN) processing unit includes an operation circuit to perform tensor operations of a given layer of a neural network in one of a first number representation and a second number representation. The NN processing unit further includes a conversion circuit coupled to at least one of an input port and an output port of the operation circuit to convert between the first number representation and the second number representation. The first number representation is one of a fixed-point number representation and a floating-point number representation, and the second number representation is the other one of the fixed-point number representation and the floating-point number representation.