Solve the Simple Equation

Can you solve below mathematical equation?

2^1234 - 2^1233




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? : 3839 :: 11 : 1209

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Crossword

The day before the 1996 U.S. presidential election, the NYT Crossword contained the clue “Lead story in tomorrow’s newspaper,” the puzzle was built so that both electoral outcomes were correct answers, requiring 7 other clues to have dual responses.