MeePythoner

What if you divide 7 by 32 in binary? $7\div32=0.21875$ Double the fractional part of the number one after another and write the result below. 1>>> $0.21875\times2=0.4375$, integral part is 0 and fractional part is 0.4375. 2>>> $0.4375\times2=0.875$, integral part is 0 and fractional part is 0.875. 3>>> $0.4375\times2=1.75$, integral part is 1 and fractional part is 0.75. 4>>> $0.75\times2=1.5$, integral part is 1 and fractional part is 0.5. 5>>> $0.5\times2=1.0$, integral part is 1 and fractional part is 0. The binary number you want is the integer parts from the top. So equivalent binary of fractional is 0.00111. When the denominator is a power of 2, it is easier to convert. $$ \begin{aligned} \dfrac{7}{32}&=\dfrac{4}{32}+\dfrac{2}{32}+\dfrac{1}{32}\\ &=\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}\\ &=\dfrac{1}{2^3}+\dfrac{1}{2^4}+\dfrac{1}{2^5}\\ &=0.00111\ (2) \end{aligned} $$ So equivalent binary of fractional ...