Latest MBA Aptitude Question SOLUTION: How many times would zero be used while writing all the natural numbers from 1 to 63 in the Binary System? (a) 32 (b) 80 (c) 111 (d) 129

1) a
2) b
3) c
4

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(#M40014054) MBA question number systems, progressions Keep an EYE

How many times would zero be used while writing all the natural numbers from 1 to 63 in the Binary System?
(a) 32 (b) 80 (c) 111 (d) 129

1) a
2) b
3) c
4) d

Asked In MBA (12 years ago)

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Arush Sharma  (8 years ago)

How many times would zero be used while writing all the natural numbers from 1 to 63 in the Binary System?

whats the approach??


For 1 to 63 in binary, the number wud have 6 digits

xxxxxx

Case 1 = xxxxx0

To find the number of such combinations, any number preceding 0 can be either 1 or 0 but all of them cannot be zero at the same time

Hence total number of such numbers is 2^5-1 = 31

Case 2 -xxxx0x

The 4 places preceeding zero can be anything but cannot be all zero

hence 2^4-1 = 15 and the last place can be 0/1 = 2 ways

total 15*2 = 30 ways

Similary, the cases would be

(2^3-1)*4= 28
(2^2-1)*8 = 24
(2-1)*16 = 16

Hence total number of zeroes = 31+30+28+24+16 = 129

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