#Number System

Question

For a floating point representation with 64 bits in the mantissa and $12$ bits in the unbiased exponent, the number of significant digits in decimal and the maximum (positive) value of the exponent in decimal will be  _______________________

Answer 1

The number of significant digits x in $64$ bits can be found as:
$10^{x} = 2^{64}$

$=>x = 19.$
The maximum value of the exponent y in $12$ bits can be found as: $10^{y} = 2^{2047}$

$=> y = 616.$
[maximum positive number in $12$ bit $2’s$ complement is $2047$]

for more :https://nptel.ac.in/content/storage2/courses/106105163/ASSIGNMENT-SOLUTION-WEEK8.pdf