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 be represented as 11111101011.

Option (B) is correct.

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