Question

The decimal number equivalent of the hexadecimal number $\underset{23ZEROS}{\underset{}{\left(\mathrm{100....001}\right)}}16$ is

• A. $2^{23}+1$
• B. $2^{24}+1$
• C. $2^{92}+1$
• D. $2^{96}+1$

Answer 1

The correct option is D $2^{96}+1$

${\left(\mathrm{10000....001}\right)}_{16}$-It has $23$ zeroes

${\left(\mathrm{10000....001}\right)}_{16}=1\times {16}^{24}+0\times {16}^{23}+....+0\times {16}^2+0\times {16}^1+1\times {16}^0$

$={16}^{24}+1$$=2^{96}+1$