Braking system with two pressure sources, and method for operating a braking system with two pressure sources

A braking system comprising four hydraulically actuatable wheel brakes, wherein one normally closed outlet valve is assigned to each wheel brake and one normally open inlet valve is assigned to each wheel brake, wherein two pressure supply devices are provided for active pressure build-up in the wheel brakes, wherein a first brake circuit and a second brake circuit are hydraulically configured with two wheel brakes of the four hydraulically actuatable wheel brakes, respectively, wherein a first pressure supply device is hydraulically connected to the two wheel brakes of the first brake circuit and a second pressure supply device is hydraulically connected to the two wheel brakes of the second brake circuit, wherein a first and a second control and regulating unit are provided, wherein the first control and regulating unit electrically controls the pressure supply device of the first brake circuit, and wherein the second control and regulating unit electrically controls the pressure supply device of the second brake circuit, wherein the two control and regulating units are connected together via a data interface, and wherein the two brake circuits are connected in hydraulically isolatable fashion by way of two normally closed circuit switch-on valves, wherein a first normally closed circuit switch-on valve of two normally closed circuit switch-on valves is configured to be controlled by the first control and regulating unit, and wherein a second normally closed circuit switch-on valve of the two normally closed circuit switch-on valves is configured to be controlled by the second control and regulating unit, and wherein precisely one normally closed outlet valve of the normally closed outlet valves in the second brake circuit is configured to be controlled by the first control and regulating unit, and wherein precisely one normally closed outlet valve of the normally closed outlet valves in the first brake circuit is configured to be controlled by the second control and regulating unit.