To convert a positive decimal fraction $x<mn\; id="EditorElement\_8293165">1</mn>$ to its binary equivalent

$x=(a_1{a}_2{a}_3$dots${)}_2$

begin by writing

$x=a_1*2^{-1}+a_2*2^{-2}+a_3*2^{-3}+$cdots

Based on this, use the following algorithm.

$($i$)x_1$:$=x$;$j$:$=1$

$($ii$)$ While $x_{j}0,$ Do the following:

$a_j$:$=$ Integer part $of2*x_j$

$x_{j+1}$:$=$ Fractional part $of2*x_j$

$j$:$=j+1$

While

End While

Apply this algorithm to convert the following decimal numbers to their binary equivalents.

$($a$)\mathrm{.}8125$

$($b$)12\mathrm{.}0625$

$($c$)\mathrm{.}1$

$($d$)\mathrm{.}2$

$($e$)\mathrm{.}4$

$($f$)\frac{1}{7}=\mathrm{.}142857142857$dots