Simplify this expression:
2^23 - 2^22 - 2^21 - 1
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1 + 2 + 2^2 + ... + 2^20
The numerator is (4-3)*2^21-1 and the denominator is 2^21-1. The numerator is equal to the denominator so the fraction equals 1.
The (4-3) is based on the binary numbers 100 and 11. Multiplying by 2^21 shifts it so the power zero is shifted to power 21, etc. The -1 in the denominator is based on repunit binary numbers are 1 less than 2^next power position in the binary representation.
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Posted by Charlie
on 2024-06-16 14:45:51 |
solution
