The number of digit 1 present in the binary representation of
3 × 512 + 7 × 64 + 5 × 8 + 3
(A)
8
(B)
9
(C)
10
(D)
12
Answer: (B)
Explanation:
3 × 512 + 7 × 64 + 5 × 8 + 3 = (2 + 1)× 512 + (4 + 2 + 1)× 64 + (4 + 1)× 8 + 2 + 1
= 1024 + 512 + 64 x 4 + 64 x 2 + 64 + 32 + 8 + 2 + 1 = 1024 + 512 + 256 + 128 + 64 + 32 + 8 + 2 + 1 As 1024 has ten 0\’s followed by 1, 512 has nine 0\’s followed by 1 and so on.. So, the expression will contain total nine 1\’s and will be represented as 11111101011. Option (B) is correct.
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