Maximum number that can be represented with $n-bits$ in base $x$ $= x^n - 1$
Maximum no. with $25$ bits in $base-10$ $=$ $10^{25}-1$ and maximum number with $k$ bits in $base-2$ $= 2^x-1$
In order to be able to be represent every $25-bit$ decimal number with $k$ bits in binary $10^{25}-1 \leq 2^k -1$
$log_{2}(10^{25} ) \leq k$
$25*log_2{10} \leq k$
$k \geq 83.048$ $\rightarrow$ $k = 84$