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

• 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
• 7 years agoHelpfull: Yes(0) No(0)