Googolmania

Define f(n) = the number of 0s before the last 1 in the binary representation of n
We have
$100=11\mathbf{\text{00}}{100}_2\Rightarrow f(100)=2$
$1000=11111\mathbf{\text{0}}{1000}_2\Rightarrow f(1000)=1$
$10000=100111\mathbf{\text{000}}{10000}_2\Rightarrow f(10000)=3$

Let $\gamma ={10}^{100}$(A googol)

Find $n_1=f({10}^{\gamma })\text{ and }{n}_2=f({10}^{8\times \gamma })$

Answer format: $n_1,n_2$

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