Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
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
Practice Binary Numbers on Quantrex Academy →

More from Binary Numbers

In base -2 notation, digits are 0 and 1 only and the places go up in powers of -2 . For… Olympiad workbookThe equation 166 × 56=8590 is valid in some base b ≥ 10 (that is 1,6,5,8,9,0 are digits… Olympiad workbookConsider the sequence 1,7,8,49,50,56,57,343, … which consists of sums of distinct powers… Olympiad workbookA number N in base 10 , is 503 in base b and 305 in base b+2 . What is the product of the… Olympiad workbookA number N in base 10 , is 503 in base b and 305 in base b+2 . What is the product of the… Olympiad workbookThe equation 166 × 56=8590 is valid in some base b ≥ 10 (that is 1,6,5,8,9,0 are digits… Olympiad workbookConsider the sequence 1,7,8,49,50,56,57,343, … which consists of sums of distinct powers… Olympiad workbook Full Binary Numbers list All Olympiad workbook PYQs