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tex.tex
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\begin{align*}
101_2 &= 1\cdot2^2 + 0\cdot2^1 + 1\cdot2^0 \\
&= 4 + 0 + 1 \\
&= 5_{10}
\end{align*}
\begin{align*}
101.1_2 &= 1\cdot2^2 + 0\cdot2^1 + 1\cdot2^0 + 1\cdot2^{-1} \\
&= 4 + 0 + 1 + \frac{1}{2} \\
&= 5.5_{10} \\
\\
11.1101_2 &= 1\cdot2^1 + 1\cdot2^0 + 1\cdot2^{-1} + 1\cdot2^{-2} + 0\cdot2^{-3} + 1\cdot2^{-4}\\
&= 2 + 1 + \frac{1}{2} + \frac{1}{4} + \frac{0}{8} + \frac{1}{16}\\
&= 3.8125_{10}
\end{align*}
(-1)^{b_{31}}\cdot(1.b_{22}b_{21}...b_0)_2\cdot2^{exp-127}
\begin{align*}
0\ 01111111\ 00000000000000000000000 &= (-1)^0 \cdot 1.00000000000000000000000_2 \cdot 2 ^ {127 - 127} \\
&= 1 \cdot 1 \cdot 2 ^ 0 \\
&= 1_{10}
\end{align*}
\begin{align*}
0\ 10000011\ 10100000000000000000000 &= (-1)^0 \cdot 1.10100000000000000000000_2 \cdot 2 ^ {131 - 127}\\
&= 1 \cdot 1.625 \cdot 2^4 \\
&= 26_{10}
\end{align*}
\begin{align*}
0\ 10000011\ 10100000000000000000000 &= (-1)^0 \cdot 1.10100000000000000000000_2 \cdot 2 ^ {131 - 127}\\
&= 1.1010_2 \cdot 2^4 \\
&= 11010_2\\
&= 26_{10}
\end{align*}
m\cdot2^n
b_{30}b_{29}...b_{23}
c_{30}c_{29}...c_{23}