If the District of Columbia convention center is built, Woodward & Lothrop will tear down its north building downtown to make way for a major new development, Woodies' Chairman Edwin K. Hoffman said yesterday.

The old north store, across G Street N.W., from the main Woodward & Lothrop department store, and the whole block it sits on will probably be redeveloped, Hoffman told shareholders at the company's annual meeting.

Hoffman predicted the rebuilding of the block, much of it owned by the company, after a shareholder questioned whether the north building was being used effectively.

"We delayed putting a lot of money into the north building for a couple of reasons," mainly the convention center question, Hoffman replied.

If the project is approved, the old Woodies building will be "kitty corner" from it, said Hoffman. With the convention center, "that building has got to come down, it's very valuable real estate."

Hoffman was elected chairman of the board of the Washington department store chain at a directors meeting that followed the shareholders' gathering. He succeeds A. Lothrop Luttrell, grandson of Alvin Mason Lothrop, one of the founders, who has been chairman since 1965.

Succeeding Hoffman as president of Woodies is Waldo H. Burnside, who has been executive vice president since 1974. Under the new division of responsibility, Burnside will be in charge of merchandising - buying, selling and marketing - and branch stores, and Hoffman will remain chief executive officer in charge of operations, finance, personnel and corporate matters.

For the first quarter ended April 30, sales increased 1 percent, from $54.7 million to $55.2 million, but profits decreased from $1.4 million (60 cents per share) to $1.2 million (51 cents), Burnside reported.