Question Number 215492 by BaliramKumar last updated on 08/Jan/25
Commented by BaliramKumar last updated on 08/Jan/25
$${Decimal}\:\:{to}\:{binary} \\ $$
Answered by ajfour last updated on 08/Jan/25
$$\mathrm{26}=\mathrm{16}+\mathrm{8}+\mathrm{0}+\mathrm{2}+\mathrm{0}=\left(\mathrm{11010}\right)_{\mathrm{2}} \\ $$$$\:\:\:\:\left(\frac{\mathrm{1}}{\mathrm{2}}\right)+\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\mathrm{0}+\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{4}} +\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{5}} +… \\ $$$$\:\:\:\:\:\:\:\:\:\:=\mathrm{0}.\mathrm{500000}+\mathrm{0}.\mathrm{250000}+\mathrm{0}+\mathrm{0}.\mathrm{062500} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\mathrm{0}.\mathrm{031250}+\mathrm{0}.\mathrm{015625}+… \\ $$$$\:\:\:\:\:\:\:\:=\mathrm{0}.\mathrm{812500}+\mathrm{0}.\mathrm{031250}+\mathrm{0}.\mathrm{015625}+.. \\ $$$$\:\:\:\:\:\:\:\:=\mathrm{0}.\mathrm{843750}+\mathrm{0}.\mathrm{015625}+..=\mathrm{0}.\mathrm{859357}+.. \\ $$$$\:{hence}\:\:\mathrm{0}.\mathrm{85}\approx\left(\mathrm{0}.\mathrm{11011}\right)_{\mathrm{2}} \\ $$$$\mathrm{26}.\mathrm{85}=\left(\mathrm{11010}.\mathrm{11011}\right)_{\mathrm{2}} \\ $$$$\:\left({B}\right)\:\checkmark \\ $$