diff --git a/custom_components/xiaomi_home/binary_sensor.py b/custom_components/xiaomi_home/binary_sensor.py
index 8019104..b2d00b6 100644
--- a/custom_components/xiaomi_home/binary_sensor.py
+++ b/custom_components/xiaomi_home/binary_sensor.py
@@ -70,8 +70,8 @@ async def async_setup_entry(
     for miot_device in device_list:
         if miot_device.miot_client.display_binary_bool:
             for prop in miot_device.prop_list.get('binary_sensor', []):
-                new_entities.append(BinarySensor(
-                    miot_device=miot_device, spec=prop))
+                new_entities.append(
+                    BinarySensor(miot_device=miot_device, spec=prop))
 
     if new_entities:
         async_add_entities(new_entities)
@@ -90,7 +90,7 @@ class BinarySensor(MIoTPropertyEntity, BinarySensorEntity):
     def is_on(self) -> bool:
         """On/Off state. True if the binary sensor is on, False otherwise."""
         if self.spec.name == 'contact-state':
-            return self._value is False
+            return bool(self._value) is False
         elif self.spec.name == 'occupancy-status':
             return bool(self._value)
         return self._value is True
diff --git a/custom_components/xiaomi_home/miot/miot_client.py b/custom_components/xiaomi_home/miot/miot_client.py
index f8f3141..e6fe6a8 100644
--- a/custom_components/xiaomi_home/miot/miot_client.py
+++ b/custom_components/xiaomi_home/miot/miot_client.py
@@ -1374,10 +1374,13 @@ class MIoTClient:
         """Update cloud devices.
         NOTICE: This function will operate the cloud_list
         """
-        # MIoT cloud service may not publish the online state updating message
+        # MIoT cloud may not publish the online state updating message
         # for the BLE device. Assume that all BLE devices are online.
+        # MIoT cloud does not publish the online state updating message for the
+        # child device under the proxy gateway (eg, VRF air conditioner
+        # controller). Assume that all proxy gateway child devices are online.
         for did, info in cloud_list.items():
-            if did.startswith('blt.'):
+            if did.startswith('blt.') or did.startswith('proxy.'):
                 info['online'] = True
         for did, info in self._device_list_cache.items():
             if filter_dids and did not in filter_dids:
diff --git a/custom_components/xiaomi_home/miot/miot_mips.py b/custom_components/xiaomi_home/miot/miot_mips.py
index 8c51c8b..6e7186d 100644
--- a/custom_components/xiaomi_home/miot/miot_mips.py
+++ b/custom_components/xiaomi_home/miot/miot_mips.py
@@ -998,9 +998,11 @@ class MipsCloudClient(_MipsClient):
                     did, MIoTDeviceState.ONLINE if msg['event'] == 'online'
                     else MIoTDeviceState.OFFLINE, ctx)
 
-        if did.startswith('blt.'):
-        # MIoT cloud may not publish BLE device online/offline state message.
-        # Do not subscribe BLE device online/offline state.
+        if did.startswith('blt.') or did.startswith('proxy.'):
+        # MIoT cloud may not publish BLE device or proxy gateway child device
+        # online/offline state message.
+        # Do not subscribe BLE device or proxy gateway child device
+        # online/offline state.
             return True
         return self.__reg_broadcast_external(
             topic=topic, handler=on_state_msg, handler_ctx=handler_ctx)
diff --git a/custom_components/xiaomi_home/miot/miot_spec.py b/custom_components/xiaomi_home/miot/miot_spec.py
index 9cabdcb..7f6a5b2 100644
--- a/custom_components/xiaomi_home/miot/miot_spec.py
+++ b/custom_components/xiaomi_home/miot/miot_spec.py
@@ -601,7 +601,10 @@ class MIoTSpecProperty(_MIoTSpecBase):
         if value is None:
             return None
         if self.format_ == int:
-            return int(round(value))
+            if self.value_range is None:
+                return int(round(value))
+            return int(
+                round(value / self.value_range.step) * self.value_range.step)
         if self.format_ == float:
             return round(value, self.precision)
         if self.format_ == bool: