Let M = 2 30 - 2 15 + 1 , and M 2 be expressed in base 2 . The number of 1 ' s in this base 2 representation of M 2 is

Question

Let M = 2 30 - 2 15 + 1 , and M 2 be expressed in base 2 . The number of 1 ' s in this base 2 representation of M 2 is, 29, 30, 59, 60

MARKS App · Accepted Answer

2 n 2 = 1 00 … 0 ⏟ n times M 2 = 2 60 - 2 46 + 2 30 - 2 16 + 2 31 + 1 = ( 11 … 1 ⏟ 14 times 00 … 0 ⏟ 46 times + 11 … 1 ⏟ 14 times 000 … 0 ⏟ 16 times + 1 00 … 0 ⏟ 31 times + 1 ) 2 Number of 1 ' s = 14 + 1 + 14 + 1 = 30

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