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In base -2 notation, digits are 0 and 1 only and the places go up in powers of -2 . For example, 11011 stands for (-2)^4+(-2)^3+(-2)^1+(-2)^0 and equals number 7 in base 10 . If the decimal number 2019 is expressed in base - 2 how many non zero digits does it contain?

Correct answer

06

Step-by-step solution

Since 2019 is closest to 2¹¹=2048 But since base is -2 Hence we will require (-2)¹² as maximum no. as well as (-2)¹¹ to compensate The series can then be worked out as the following permutation. 1100000100111 Hence no. of non zero digits =6

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