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Olympiad workbook
Exam
Olympiad workbook
Subject
IOQM
Chapter
Binary Numbers

Olympiad workbook · IOQM · Binary Numbers

In base -2 notation, digits are 0 and 1 only and the places go up...

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(-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=20482^{11}=2048 But since base is -2 Hence we will require (−2)12(-2)^{12} as maximum no. as well as (−2)11(-2)^{11} to compensate The series can then be worked out as the following permutation. 11000001001111100000100111 Hence no. of non zero digits =6=6
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