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previous
Describes something that has existed or been valid up to the present point in time. It refers to the past up to the present.
Der neue Chef hat viele Änderungen gegenüber der bisherigen Vorgehensweise eingeführt.
The new boss introduced many changes compared with the previous approach.
The word is made up of 'bis her' (until now, up to here) and the adjective ending '-ig'. So it directly describes the state that has applied “until now.”
Bis her war alles in Ordnung.
Up to now, everything was fine.
The adjective 'bisherig' (previous, up to now) is used almost exclusively before a noun (attributively). Using it as a standalone predicate, e.g. 'Der Plan war bisherig' (The plan was previous), is very unusual.
Seine bisherige Leistung war immer ausgezeichnet.
His performance so far has always been excellent.
'Bisherig' (previous) is often used to emphasize a contrast between old and new. Typical combinations are 'der bisherige Plan' (the previous plan), 'die bisherigen Ergebnisse' (the results so far), or 'der bisherige Rekord' (the previous record).
Der neue Läufer hat den bisherigen Rekord gebrochen.
The new runner broke the previous record.
so far
'bisher' and 'bisherig' both express that something applies, or has applied, up to now. The most important difference is grammar. 'bisher' is an adverb and usually describes a whole sentence or a verb: What has happened so far? 'bisherig' is an adjective and describes a noun: 'die bisherige Lösung' (the previous solution), 'der bisherige Plan' (the previous plan). Learners may confuse the words because the meaning is very close. Remember: 'bisher' often stands freely in the sentence, while 'bisherig' stands before a noun and takes an adjective ending.
Die Lehrerin ändert den bisherigen Plan, weil der Termin ausfällt.
The teacher is changing the previous plan because the appointment has been canceled.
Bisher gefällt mir der Kurs sehr gut.
So far, I like the course very much.