digital logic

Question

A decimal number has 25 digits. The number of bits required for its equivalent binary representation is approximately

1)50

2)75

3)60

4)70

Comments

try for small number like,

for 7 - 3bits

for 16 - 4bits, you will find pattern that number of bits required are floor(logn) + 1, where n is decimal number.

now with 25 bits maximum decimal number n=10²⁵-1

so, number of bits required for n = floor(log(10²⁵-1)) + 1 = 84(approx)

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@ joshi_nitish Not able to understand how are you interpreting the pattern to the best of my knowledge i interpreted the question with the maximum value that can be represented with the no of digits but it seems like its not following any pattern !Thus i was also confused with this question ! could you please tell me how you are summing up the patter?

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thanks

Answer 1

The maximum value that can be represented with 25 digits is 10²⁵-1.[The reason is  : if you have 2 digit number the maximum number that could be represented is 99 which is 10²-1 , Like we used in binary because of 0].
Now let say we need x bits to represent this number then number itself would be 2^x-1.

Therefore 10²⁵-1=2^x-1
25log₂10=x
25*3.322=x
x=83.04...