Im learning how the mantisse and exponent are working in the float representation
Ivve managed to catch the idea from here
however i have a problem analyzing a value.
from this picture :
please look at line #7 (at the right side).
they wrote :
2^(-126) = 1.18*10^(-38)
how did they do this conversion ?
can you please specify the steps for me to future convertion ? (like this)
$$2^k = (10^{\log_{10}(2)})^k = 10^{\lfloor \log_{10}(2) \cdot k \rfloor + \varepsilon} = 10^{\varepsilon} \times 10^{\lfloor \log_{10}(2) \cdot k \rfloor} $$
where $\lfloor \cdot \rfloor$ means round to $-\infty$ and $\varepsilon \in [0, 1)$ is the remaining fractional part of the exponent. Then $10^{\varepsilon} \in [1, 10)$. For $k= -126$ you get $\log_{10}(2) \cdot -126 \approx -37.9298$ and so
$$2^{-126} \approx 10^{0.0702} \times 10^{-38} \approx 1.175 \times 10^{-38}.$$