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Question Number 113134 by bemath last updated on 11/Sep/20

$$\mathrm{any}\mathrm{one}\mathrm{can}\mathrm{explain}\mathrm{me}\mathrm{how}\mathrm{to}$$$$\mathrm{change}\mathrm{decimal}\mathrm{number}\mathrm{to}$$$$\mathrm{biner}\mathrm{number}.{\mathrm{i}}^{\prime }\mathrm{m}\mathrm{forgot}.$$$$\mathrm{example}{\left(315\right)}_{10}={(...)}_2$$$$\mathrm{thank}\mathrm{you}$$

Commented by I want to learn more last updated on 11/Sep/20

$$2315\mathrm{Remainder}$$$$----\mid -----\mid --------$$$$2\mid 157\mid 1$$$$2\mid 78\mid 1$$$$2\mid 39\mid 0$$$$2\mid 19\mid 1$$$$2\mid 9\mid 1$$$$2\mid 4\mid 1$$$$2\mid 2\mid 0$$$$2\mid 1\mid 0$$$$2\mid 0\mid 1$$$$\mathrm{read}\mathrm{the}\mathrm{remainder}\mathrm{from}\mathrm{bottom}\mathrm{to}\mathrm{top}$$$${315}_{10}={100111011}_2$$

Commented by bemath last updated on 11/Sep/20

$$\mathrm{thank}\mathrm{you}\mathrm{friend}$$

Answered by MJS_new last updated on 11/Sep/20

$$\mathrm{find}\mathrm{the}\mathrm{largest}n\mathrm{with}{2}^n⩽315$$$$\Rightarrow n=8$$$${\left(315\right)}_{10}={\left(1\underset{7}{a}\underset{6}{a}\underset{5}{a}\underset{4}{a}\underset{3}{a}\underset{2}{a}\underset{1}{a}\underset{0}{a}\right)}_2$$$$315-2^8=59$$$$\mathrm{find}\mathrm{the}\mathrm{largest}n\mathrm{with}{2}^n⩽59$$$$\Rightarrow n=5$$$${\left(315\right)}_{10}={\left(1001\underset{4}{a}\underset{3}{a}\underset{2}{a}\underset{1}{a}\underset{0}{a}\right)}_2$$$$59-2^5=27$$$$...$$

Commented by bemath last updated on 11/Sep/20

$$\mathrm{thank}\mathrm{you}\mathrm{prof}$$

Answered by mr W last updated on 11/Sep/20

$$\lfloor {\log }_{2}315\rfloor =8$$$$315-2^8=59$$$$\lfloor {\log }_{2}59\rfloor =5$$$$59-2^5=27$$$$\lfloor {\log }_{2}27\rfloor =4$$$$27-2^4=11$$$$\lfloor {\log }_{2}11\rfloor =3$$$$11-2^3=3$$$$\lfloor {\log }_{2}3\rfloor =1$$$$3-2^1=1=2^0$$$$\Rightarrow 315=2^8+2^5+2^4+2^3+2^1+2^0$$$$=1\times 2^8+0\times 2^7+0\times 2^6+1\times 2^5+1\times 2^4+1\times 2^3+0\times 2^2+1\times 2^1+1\times 2^0$$$$={\left(100111011\right)}_2$$

Commented by bemath last updated on 11/Sep/20

$$\mathrm{thank}\mathrm{you}\mathrm{prof}$$

Answered by Aziztisffola last updated on 11/Sep/20

Commented by bemath last updated on 11/Sep/20

$$\mathrm{thank}\mathrm{you}\mathrm{friend}$$

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