NIELIT 2017 OCT Scientific Assistant A (CS) - Section B: 1

Question

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

• A. $50$
• B. $74$
• C. $40$
• D. $60$

Answer 1

Consider three digits of decimal numbers.Maximum number, we can generate by that three digits are 103-1 which is 999.
Then, Decimal number has 25 digits, so maximum number is $10^{25} -1$
Similarly, in the binary representation with "n" bits the maximum number is $2^{n} -1$
So we can write $10^{25} -1 = 2^{n} - 1 $

$10^{25} = 2 ^{n}$   After taking log 2 on both sides
$log 2^{n}=log 10^{25}$
$n log 2=25 log10$
$n=25*(3.322)/ log 2$
n=83