
down
A colloquial expression for a state of emotional dejection, sadness, or lack of energy.
Nach der Absage war er den ganzen Tag ziemlich down.
After the rejection, he was pretty down all day.
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A colloquial expression for a state of emotional dejection, sadness, or lack of energy.
Nach der Absage war er den ganzen Tag ziemlich down.
After the rejection, he was pretty down all day.

In technology, the term for the state in which a computer system, server, or network is temporarily not working or not reachable.
Wegen Wartungsarbeiten war die Webseite für eine Stunde down.
Because of maintenance work, the website was down for an hour.
The word 'down' is borrowed directly from English and is used mainly in colloquial speech. It keeps its English pronunciation.
Ich fühle mich heute irgendwie down.
I feel kind of down today.
As an adjective, 'down' is not declined and almost always comes after a verb like 'sein' (to be) or 'sich fühlen' (to feel). You cannot place it before a noun.
Der Server ist schon wieder down.
The server is down again.
You can recognize the meaning from the subject of the sentence. If 'down' refers to a person, it means 'niedergeschlagen' (dejected/down). If it refers to a technical system, it means 'außer Betrieb' (out of service/down).
Mein Freund ist seit gestern down.
My friend has been down since yesterday.
offline
Down means that a system is currently not working or cannot be reached, usually because of a malfunction. Offline only says that there is no connection to a network; this can also be intentional. Therefore, down is appropriate for a malfunction, while offline is appropriate for a deliberate disconnection.

Wegen einer technischen Störung ist der Server seit einer Stunde down.
Because of a technical problem, the server has been down for an hour.
Wegen der geplanten Wartung ist der Server seit einer Stunde offline.
Because of the scheduled maintenance, the server has been offline for an hour.