number syatem

Question

A decimal number has
25 digits. The number of bits
needed for its equivalent
binary representation is,
approximately, 
a) 50
b) 55
c) 80
d) 75
Explain??

Answer 1

Here d=digits in decimal representation

       n= bit in binary representation

d>n log10 2

 25=n*.3010

n=83 Apx

Comments

Yes even i got the same 10^d -1 = 2^b -1 where d is number of digits i

n decimal here d is 25

10^25 = 2 ^b

b= log₂(10^25)= 83.04 =83 bits approx