Explanation

127.25 = 127 + 0.25

We divide the whole number part by 2 and multiply the decimal part by 2

thus,

$\begin{array}{r|l} 2 & 127 \\ 2 & 63 \; \text{R} \; 1 \\ 2 & 31 \; \text{R} \; 1 \\ 2 & 15 \; \text{R} \; 1 \\ 2 & 7 \; \text{R} \; 1 \\ 2 & 3 \; \text{R} \; 1 \\ 2 & 1 \; \text{R} \; 1 \\ & 0 \; \text{R} \; 1 \\ \end{array} \text{Next, we multiply the decimal part by 2:} \begin{array}{r} 0.25 \times 2 = 0.50 \\ 0.50 \times 2 = 1.00 \\ \end{array} \Rightarrow 0.01_2 \text{And finally, we combine:} \Rightarrow 1111111_2 + 0.01_2 = 1111111.01_2$

127.25 = 127 + 0.25

We divide the whole number part by 2 and multiply the decimal part by 2

thus,

$\begin{array}{r|l} 2 & 127 \\ 2 & 63 \; \text{R} \; 1 \\ 2 & 31 \; \text{R} \; 1 \\ 2 & 15 \; \text{R} \; 1 \\ 2 & 7 \; \text{R} \; 1 \\ 2 & 3 \; \text{R} \; 1 \\ 2 & 1 \; \text{R} \; 1 \\ & 0 \; \text{R} \; 1 \\ \end{array} \text{Next, we multiply the decimal part by 2:} \begin{array}{r} 0.25 \times 2 = 0.50 \\ 0.50 \times 2 = 1.00 \\ \end{array} \Rightarrow 0.01_2 \text{And finally, we combine:} \Rightarrow 1111111_2 + 0.01_2 = 1111111.01_2$