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I'm trying to compute the following expression: $10101011 \cdot 1025$ in a simple, easy way without using a calculator, or an elementary school way. I realized that $1025=2^{10}+1$ so I need to compute now $10101011 \cdot 2^{10}+10101011$, How should I proceed?

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up vote 8 down vote accepted

Forget binary and use base $10$ !

$$10101011\cdot 1000= 10101011000$$ $$10101011\cdot 25=10101011\cdot 100 / 4=505050550/2=252525275$$

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