With the rapid development of modern processors, logical operation processors could not only process data by logical operations but also store the data. The logical operation processor designed in this paper will be the bit-serial logical operation processor. In order to build the processor, four units should be designed first: the Shift Register Unit, Computation Unit, Routing Unit, and Control Unit. Among them, the Register Unit and the Control Unit are the most important. For the Register Unit, there will be two 4-bit registers. For the Control Unit, this circuit will implement a Mealy machine to determine the output and state of the circuit. The input to the processor will first get into the Control Unit, and then the data given outside will be stored in the Shift Register Unit and will be input to the Computation Unit and finally returned to the Shift Register Unit after Routing Unit. Since the processor is operating in series, the Control Unit and the Shift Register Unit should work synchronously.