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Are the Keysight 531xxA and 53200 Series frequency counter inputs floating or grounded?

The counter inputs are not floating -- the BNC shield (shell) is at chassis ground (earth ground).

The new 53210A, 53220A and 53230A frequency counters offer an optional battery (Option 300) for portability and timebase accuracy and stability. Under battery power, the instrument chassis, may float to the potential of the measured signal supplied by the user. Connect the instrument chassis to earth ground during battery operation.