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Question Number 113199 by Rasheed.Sindhi last updated on 11/Sep/20

$$Changethefollowingdecimal$$$$numberintobinarynumber:$$$$73.108$$

Commented by bemath last updated on 11/Sep/20

$$\mathrm{what}\mathrm{is}\mathrm{binary}\mathrm{one}\mathrm{sir}?$$

Commented by Rasheed.Sindhi last updated on 11/Sep/20

$$Readthequestionnow.$$

Commented by bemath last updated on 11/Sep/20

$$\mathrm{ok}\mathrm{sir}.\mathrm{santuyy}$$

Commented by Rasheed.Sindhi last updated on 11/Sep/20

$${What}^{\prime }sthemeaningof$$$$‘‘{\mathrm{santuyy}}^{″}?$$

Commented by 1549442205PVT last updated on 12/Sep/20

$$\mathrm{It}\mathrm{is}\mathrm{counting}\mathrm{system}\mathrm{of}\mathrm{base}2.\mathrm{As}\mathrm{I}$$$$\mathrm{known},\mathrm{currently}\mathrm{we}\mathrm{are}\mathrm{using}$$$$\mathrm{countimg}\mathrm{system}\mathrm{of}\mathrm{base}10,\mathrm{is}\mathrm{also}$$$$\mathrm{called}\mathrm{the}\mathrm{decimal}\mathrm{system}\mathrm{that}\mathrm{uses}\mathrm{ten}$$$$\mathrm{symbols}:0,1,...,9\mathrm{to}\mathrm{represent}\mathrm{numbers}$$$$.\mathrm{The}\mathrm{counting}\mathrm{system}\mathrm{of}\mathrm{base}2\mathrm{is}\mathrm{also}$$$$\mathrm{called}\mathrm{the}\mathrm{binary}\mathrm{system}\mathrm{that}\mathrm{uses}$$$$\mathrm{only}\mathrm{two}\mathrm{sumbols}0\mathrm{and}1\mathrm{to}\mathrm{represent}$$$$\mathrm{numbers}.\mathrm{It}\mathrm{is}\mathrm{used}\mathrm{in}\mathrm{computer}$$$$\mathrm{science}\mathrm{and}\mathrm{digital}\mathrm{technology}$$$$\mathrm{Converts}\mathrm{decimal}\mathrm{to}\mathrm{binary}-\mathrm{odd}\mathrm{part}$$$$1)\mathrm{Procedure}$$$$\bullet \mathrm{Step}1:\mathrm{We}\mathrm{multiply}\mathrm{the}\mathrm{odd}\mathrm{part}\mathrm{by}$$$$\mathrm{a}\mathrm{power}\mathrm{of}2(\mathrm{say}{2}^{\mathrm{n}},\mathrm{n}>1)$$$$\bullet \mathrm{Step}2:\mathrm{get}\mathrm{the}\mathrm{result}\mathrm{in}\mathrm{step}1(\mathrm{only}$$$$\mathrm{take}\mathrm{whole}\mathrm{part})\mathrm{and}\mathrm{then}\mathrm{convert}\mathrm{to}$$$$\mathrm{binary}$$$$\bullet \mathrm{Step}3:\mathrm{divide}\mathrm{the}\mathrm{result}\mathrm{in}\mathrm{step}2\mathrm{by}{2}^{\mathrm{n}}$$$$,\mathrm{we}\mathrm{get}\mathrm{odd}\mathrm{part}\mathrm{in}\mathrm{binary}\mathrm{form}$$$$(\mathrm{essentially}\mathrm{this}\mathrm{step}\mathrm{is}\mathrm{to}\mathrm{move}\mathrm{the}$$$$\mathrm{comma}\mathrm{to}\mathrm{the}\mathrm{left}\mathrm{n}\mathrm{times})$$$$2)\mathrm{For}\mathrm{example}$$$$\bullet \mathrm{Ex}1:\mathrm{Convert}2.5625\mathrm{to}\mathrm{binary}$$$$2_{10}={10}_2$$$$-\mathrm{Multiply}:.5625\ast \left(2^4\right)=9$$$$-\mathrm{Convert}9\mathrm{to}\mathrm{binary}:9_{10}={1001}_2$$$$-\mathrm{Divide}:{1001}_2/\left(2^4\right)=.1001$$$$\Rightarrow 2.{5625}_{10}=10.{1001}_2$$$$\bullet \mathrm{Ex}2:\mathrm{Convert}2.3333\mathrm{to}\mathrm{binary}$$$$2_{10}={10}_2$$$$-\mathrm{Multiply}:.3333\ast \left(2^{16}\right)=21843.1488$$$$-\mathrm{Convert}21843\mathrm{to}\mathrm{binary}:$$$${21843}_{10}=0101010101010011$$$$-\mathrm{divide}0101010101010011/2^{16}$$$$=.0101010101010011$$$$\Rightarrow 2.{3333}_{10}=10.{0101010101010011}_2$$$$\bullet \mathrm{Ex}3:\mathrm{convert}2.6973\mathrm{to}\mathrm{binary}$$$$2_{10}={10}_2$$$$-\mathrm{Multiply}:.6973\ast \left(2^{15}\right)=22849.1264$$$$-\mathrm{convert}22849\mathrm{to}\mathrm{binary}:$$$${22849}_{10}={101100101000001}_2$$$$-\mathrm{dovide}{101100101000001}_2/2^{15}$$$$=.{101100101000001}_2$$$$\Rightarrow 2.{6973}_{10}=10.{101100101000001}_2$$

Commented by Rasheed.Sindhi last updated on 12/Sep/20

$$\mathcal{T}hanksfordetailledanswer.$$

Commented by Rasheed.Sindhi last updated on 12/Sep/20

$$By{}^{\prime }odd{part}^{\prime }doyoumean$$$$\text{You can't use 'macro parameter character \#' in math mode}$$

Commented by 1549442205PVT last updated on 12/Sep/20

$$\mathrm{Ok},\mathrm{is}\mathrm{also}\mathrm{called}\mathrm{decimal}\mathrm{part}\mathrm{of}\mathrm{a}$$$$\mathrm{number}.\mathrm{Ex}:12.34567245\mathrm{then}\mathrm{its}$$$$‘‘\mathrm{odd}{\mathrm{part}}^{″}\mathrm{is}.34567245$$

Answered by Aziztisffola last updated on 11/Sep/20

$$73.108=73+0.108$$$${\left(73\right)}_{10}\Rightarrow {\left(\mathrm{x}\right)}_2\mathrm{and}{(0.108)}_{10}\Rightarrow {(0.\mathrm{y})}_2$$$$\Rightarrow {(73.108)}_{10}={(\mathrm{x}.\mathrm{y})}_2$$$$\frac{73}{2}\Rightarrow \mathrm{q}=36\mathrm{\&}\mathrm{r}=1$$$$\frac{36}{2}\Rightarrow \mathrm{q}=18\mathrm{\&}\mathrm{r}=1$$$$\frac{18}{2}\Rightarrow \mathrm{q}=9\mathrm{\&}\mathrm{r}=0$$$$\frac{9}{2}\Rightarrow \mathrm{q}=4\mathrm{\&}\mathrm{r}=1$$$$\frac{4}{2}\Rightarrow \mathrm{q}=2\mathrm{\&}\mathrm{r}=0$$$$\frac{2}{2}\Rightarrow \mathrm{q}=1\mathrm{\&}\mathrm{r}=0$$$${\left(73\right)}_{10}={\left(1001001\right)}_2={\left(\mathrm{x}\right)}_2$$$$0.108\times 2=0.216$$$$1-0.216=0.784$$$$0.784\times 2=1.568$$$$0.568\times 2=1.136$$$$0.136\times 2=0.272$$$$1-0.272=0.728$$$$0.728\times 2=1.456$$$$0.456\times 2=0.912$$$$.......$$$$.......$$$${(0.108)}_{10}={(0.011010...)}_2={(0.\mathrm{y})}_2$$$$\mathrm{then}{(73.108)}_{10}={(1001001.011010...)}_2$$

Commented by Rasheed.Sindhi last updated on 12/Sep/20

$$\mathcal{T}hanksmiss.$$

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