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Question Number 113199 by Rasheed.Sindhi last updated on 11/Sep/20
Change the following decimal number into binary number: 73.108
$${Change}\:{the}\:{following}\:{decimal} \\ $$$${number}\:{into}\:{binary}\:{number}: \\ $$$$\mathrm{73}.\mathrm{108} \\ $$
Commented by bemath last updated on 11/Sep/20
what is binary one sir?
$$\mathrm{what}\:\mathrm{is}\:\mathrm{binary}\:\mathrm{one}\:\mathrm{sir}? \\ $$
Commented by Rasheed.Sindhi last updated on 11/Sep/20
Read the question now.
$${Read}\:{the}\:{question}\:{now}. \\ $$
Commented by bemath last updated on 11/Sep/20
ok sir. santuyy
$$\mathrm{ok}\:\mathrm{sir}.\:\mathrm{santuyy} \\ $$
Commented by Rasheed.Sindhi last updated on 11/Sep/20
What′s the meaning of “santuyy”?
$${What}'{s}\:{the}\:{meaning}\:{of} \\ $$$$“\mathrm{santuyy}''? \\ $$
Commented by 1549442205PVT last updated on 12/Sep/20
It is counting system of base 2.As I known ,currently we are using countimg system of base 10 ,is also called the decimal system that uses ten symbols :0,1,...,9 to represent numbers .The counting system of base 2 is also called the binary system that uses only two sumbols 0 and 1 to represent numbers.It is used in computer science and digital technology Converts decimal to binary−odd part 1)Procedure •Step 1:We multiply the odd part by a power of 2(say 2^n ,n>1) •Step 2:get the result in step 1 (only take whole part)and then convert to binary •Step 3:divide the result in step 2 by 2^n ,we get odd part in binary form (essentially this step is to move the comma to the left n times) 2)For example •Ex1:Convert 2.5625 to binary 2_(10) =10_2 −Multiply :.5625 ∗(2^4 )=9 −Convert 9 to binary:9_(10) =1001_2 −Divide:1001_2 /(2^4 )=.1001 ⇒2.5625_(10) =10.1001_2 •Ex2:Convert 2.3333 to binary 2_(10) =10_2 −Multiply:.3333∗(2^(16) )=21843.1488 −Convert 21843 to binary: 21843_(10) =0101010101010011 −divide 0101010101010011/2^(16) =.0101010101010011 ⇒2.3333_(10) =10.0101010101010011_2 •Ex3:convert 2.6973 to binary 2_(10) =10_2 −Multiply :.6973 ∗(2^(15) )=22849.1264 −convert 22849 to binary: 22849_(10) =101100101000001_2 −dovide 101100101000001_2 /2^(15) =.101100101000001_2 ⇒2.6973_(10) =10.101100101000001_2
$$\mathrm{It}\:\mathrm{is}\:\mathrm{counting}\:\mathrm{system}\:\mathrm{of}\:\mathrm{base}\:\mathrm{2}.\mathrm{As}\:\mathrm{I} \\ $$$$\mathrm{known}\:,\mathrm{currently}\:\mathrm{we}\:\mathrm{are}\:\mathrm{using} \\ $$$$\mathrm{countimg}\:\mathrm{system}\:\mathrm{of}\:\mathrm{base}\:\mathrm{10}\:,\mathrm{is}\:\mathrm{also} \\ $$$$\mathrm{called}\:\mathrm{the}\:\mathrm{decimal}\:\mathrm{system}\:\mathrm{that}\:\mathrm{uses}\:\mathrm{ten}\: \\ $$$$\mathrm{symbols}\::\mathrm{0},\mathrm{1},…,\mathrm{9}\:\mathrm{to}\:\mathrm{represent}\:\mathrm{numbers} \\ $$$$.\mathrm{The}\:\mathrm{counting}\:\mathrm{system}\:\mathrm{of}\:\mathrm{base}\:\mathrm{2}\:\mathrm{is}\:\mathrm{also} \\ $$$$\mathrm{called}\:\mathrm{the}\:\mathrm{binary}\:\mathrm{system}\:\mathrm{that}\:\mathrm{uses} \\ $$$$\mathrm{only}\:\mathrm{two}\:\mathrm{sumbols}\:\mathrm{0}\:\mathrm{and}\:\mathrm{1}\:\mathrm{to}\:\mathrm{represent} \\ $$$$\mathrm{numbers}.\mathrm{It}\:\mathrm{is}\:\mathrm{used}\:\mathrm{in}\:\mathrm{computer} \\ $$$$\mathrm{science}\:\mathrm{and}\:\mathrm{digital}\:\mathrm{technology} \\ $$$$\mathrm{Converts}\:\mathrm{decimal}\:\mathrm{to}\:\mathrm{binary}−\mathrm{odd}\:\mathrm{part} \\ $$$$\left.\mathrm{1}\right)\mathrm{Procedure} \\ $$$$\bullet\mathrm{Step}\:\mathrm{1}:\mathrm{We}\:\mathrm{multiply}\:\mathrm{the}\:\mathrm{odd}\:\mathrm{part}\:\mathrm{by} \\ $$$$\mathrm{a}\:\mathrm{power}\:\mathrm{of}\:\mathrm{2}\left(\mathrm{say}\:\mathrm{2}^{\mathrm{n}} ,\mathrm{n}>\mathrm{1}\right) \\ $$$$\bullet\mathrm{Step}\:\mathrm{2}:\mathrm{get}\:\mathrm{the}\:\mathrm{result}\:\mathrm{in}\:\mathrm{step}\:\mathrm{1}\:\left(\mathrm{only}\right. \\ $$$$\left.\mathrm{take}\:\mathrm{whole}\:\mathrm{part}\right)\mathrm{and}\:\mathrm{then}\:\mathrm{convert}\:\mathrm{to} \\ $$$$\mathrm{binary} \\ $$$$\bullet\mathrm{Step}\:\mathrm{3}:\mathrm{divide}\:\mathrm{the}\:\mathrm{result}\:\mathrm{in}\:\mathrm{step}\:\mathrm{2}\:\mathrm{by}\:\mathrm{2}^{\mathrm{n}} \\ $$$$,\mathrm{we}\:\mathrm{get}\:\mathrm{odd}\:\mathrm{part}\:\mathrm{in}\:\mathrm{binary}\:\mathrm{form} \\ $$$$\left(\mathrm{essentially}\:\mathrm{this}\:\mathrm{step}\:\mathrm{is}\:\mathrm{to}\:\mathrm{move}\:\mathrm{the}\right. \\ $$$$\left.\mathrm{comma}\:\mathrm{to}\:\mathrm{the}\:\mathrm{left}\:\mathrm{n}\:\mathrm{times}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{For}\:\mathrm{example} \\ $$$$\bullet\mathrm{Ex1}:\mathrm{Convert}\:\mathrm{2}.\mathrm{5625}\:\mathrm{to}\:\mathrm{binary} \\ $$$$\mathrm{2}_{\mathrm{10}} =\mathrm{10}_{\mathrm{2}} \\ $$$$−\mathrm{Multiply}\::.\mathrm{5625}\:\ast\left(\mathrm{2}^{\mathrm{4}} \right)=\mathrm{9} \\ $$$$−\mathrm{Convert}\:\mathrm{9}\:\mathrm{to}\:\mathrm{binary}:\mathrm{9}_{\mathrm{10}} =\mathrm{1001}_{\mathrm{2}} \\ $$$$−\mathrm{Divide}:\mathrm{1001}_{\mathrm{2}} /\left(\mathrm{2}^{\mathrm{4}} \right)=.\mathrm{1001} \\ $$$$\Rightarrow\mathrm{2}.\mathrm{5625}_{\mathrm{10}} =\mathrm{10}.\mathrm{1001}_{\mathrm{2}} \\ $$$$\bullet\mathrm{Ex2}:\mathrm{Convert}\:\mathrm{2}.\mathrm{3333}\:\mathrm{to}\:\mathrm{binary} \\ $$$$\mathrm{2}_{\mathrm{10}} =\mathrm{10}_{\mathrm{2}} \\ $$$$−\mathrm{Multiply}:.\mathrm{3333}\ast\left(\mathrm{2}^{\mathrm{16}} \right)=\mathrm{21843}.\mathrm{1488} \\ $$$$−\mathrm{Convert}\:\mathrm{21843}\:\mathrm{to}\:\mathrm{binary}: \\ $$$$\mathrm{21843}_{\mathrm{10}} =\mathrm{0101010101010011} \\ $$$$−\mathrm{divide}\:\mathrm{0101010101010011}/\mathrm{2}^{\mathrm{16}} \\ $$$$=.\mathrm{0101010101010011} \\ $$$$\Rightarrow\mathrm{2}.\mathrm{3333}_{\mathrm{10}} =\mathrm{10}.\mathrm{0101010101010011}_{\mathrm{2}} \\ $$$$\bullet\mathrm{Ex3}:\mathrm{convert}\:\mathrm{2}.\mathrm{6973}\:\mathrm{to}\:\mathrm{binary} \\ $$$$\mathrm{2}_{\mathrm{10}} =\mathrm{10}_{\mathrm{2}} \\ $$$$−\mathrm{Multiply}\::.\mathrm{6973}\:\ast\left(\mathrm{2}^{\mathrm{15}} \right)=\mathrm{22849}.\mathrm{1264} \\ $$$$−\mathrm{convert}\:\mathrm{22849}\:\mathrm{to}\:\mathrm{binary}: \\ $$$$\mathrm{22849}_{\mathrm{10}} =\mathrm{101100101000001}_{\mathrm{2}} \\ $$$$−\mathrm{dovide}\:\mathrm{101100101000001}_{\mathrm{2}} /\mathrm{2}^{\mathrm{15}} \\ $$$$=.\mathrm{101100101000001}_{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{2}.\mathrm{6973}_{\mathrm{10}} =\mathrm{10}.\mathrm{101100101000001}_{\mathrm{2}} \\ $$
Commented by Rasheed.Sindhi last updated on 12/Sep/20
Thanks for detailled answer.
$$\mathcal{T}{hanks}\:{for}\:{detailled}\:{answer}. \\ $$
Commented by Rasheed.Sindhi last updated on 12/Sep/20
By ′odd part′do you mean fractional part?(see line#11)
$${By}\:'{odd}\:{part}'{do}\:{you}\:{mean} \\ $$$${fractional}\:{part}?\left({see}\:{line}#\mathrm{11}\right) \\ $$
Commented by 1549442205PVT last updated on 12/Sep/20
Ok,is also called decimal part of a number.Ex:12.34567245 then its “odd part”is .34567245
$$\mathrm{Ok},\mathrm{is}\:\mathrm{also}\:\mathrm{called}\:\mathrm{decimal}\:\mathrm{part}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{number}.\mathrm{Ex}:\mathrm{12}.\mathrm{34567245}\:\mathrm{then}\:\mathrm{its} \\ $$$$“\mathrm{odd}\:\mathrm{part}''\mathrm{is}\:.\mathrm{34567245} \\ $$
Answered by Aziztisffola last updated on 11/Sep/20
73.108=73+0.108 (73)_(10) ⇒(x)_2 and (0.108)_(10) ⇒(0.y)_2 ⇒(73.108)_(10) =(x.y)_2 ((73)/2)⇒ q=36 & r=1 ((36)/2)⇒q=18 & r=1 ((18)/2)⇒ q=9 & r=0 (9/2)⇒ q=4 & r=1 (4/2)⇒ q=2 & r=0 (2/2)⇒ q=1 & r=0 (73)_(10) =(1001001)_2 =(x)_2 0.108×2=0.216 1−0.216=0.784 0.784×2=1.568 0.568×2=1.136 0.136×2=0.272 1−0.272=0.728 0.728×2=1.456 0.456×2=0.912 ....... ....... (0.108)_(10) =(0.011010...)_2 =(0.y)_2 then (73.108)_(10) =(1001001.011010...)_2
$$\mathrm{73}.\mathrm{108}=\mathrm{73}+\mathrm{0}.\mathrm{108} \\ $$$$\left(\mathrm{73}\right)_{\mathrm{10}} \Rightarrow\left(\mathrm{x}\right)_{\mathrm{2}} \:\:\mathrm{and}\:\left(\mathrm{0}.\mathrm{108}\right)_{\mathrm{10}} \Rightarrow\left(\mathrm{0}.\mathrm{y}\right)_{\mathrm{2}} \\ $$$$\:\Rightarrow\left(\mathrm{73}.\mathrm{108}\right)_{\mathrm{10}} =\left(\mathrm{x}.\mathrm{y}\right)_{\mathrm{2}} \\ $$$$\frac{\mathrm{73}}{\mathrm{2}}\Rightarrow\:\mathrm{q}=\mathrm{36}\:\&\:\mathrm{r}=\mathrm{1} \\ $$$$\frac{\mathrm{36}}{\mathrm{2}}\Rightarrow\mathrm{q}=\mathrm{18}\:\:\&\:\mathrm{r}=\mathrm{1} \\ $$$$\frac{\mathrm{18}}{\mathrm{2}}\Rightarrow\:\mathrm{q}=\mathrm{9}\:\&\:\mathrm{r}=\mathrm{0} \\ $$$$\frac{\mathrm{9}}{\mathrm{2}}\Rightarrow\:\mathrm{q}=\mathrm{4}\:\&\:\mathrm{r}=\mathrm{1} \\ $$$$\frac{\mathrm{4}}{\mathrm{2}}\Rightarrow\:\mathrm{q}=\mathrm{2}\:\&\:\mathrm{r}=\mathrm{0} \\ $$$$\frac{\mathrm{2}}{\mathrm{2}}\Rightarrow\:\mathrm{q}=\mathrm{1}\:\&\:\mathrm{r}=\mathrm{0} \\ $$$$\:\left(\mathrm{73}\right)_{\mathrm{10}} =\left(\mathrm{1001001}\right)_{\mathrm{2}} =\left(\mathrm{x}\right)_{\mathrm{2}} \\ $$$$\mathrm{0}.\mathrm{108}×\mathrm{2}=\mathrm{0}.\mathrm{216} \\ $$$$\mathrm{1}−\mathrm{0}.\mathrm{216}=\mathrm{0}.\mathrm{784} \\ $$$$\mathrm{0}.\mathrm{784}×\mathrm{2}=\mathrm{1}.\mathrm{568} \\ $$$$\mathrm{0}.\mathrm{568}×\mathrm{2}=\mathrm{1}.\mathrm{136} \\ $$$$\mathrm{0}.\mathrm{136}×\mathrm{2}=\mathrm{0}.\mathrm{272} \\ $$$$\mathrm{1}−\mathrm{0}.\mathrm{272}=\mathrm{0}.\mathrm{728} \\ $$$$\mathrm{0}.\mathrm{728}×\mathrm{2}=\mathrm{1}.\mathrm{456} \\ $$$$\mathrm{0}.\mathrm{456}×\mathrm{2}=\mathrm{0}.\mathrm{912} \\ $$$$……. \\ $$$$……. \\ $$$$\left(\mathrm{0}.\mathrm{108}\right)_{\mathrm{10}} =\left(\mathrm{0}.\mathrm{011010}…\right)_{\mathrm{2}} =\left(\mathrm{0}.\mathrm{y}\right)_{\mathrm{2}} \\ $$$$\mathrm{then}\:\left(\mathrm{73}.\mathrm{108}\right)_{\mathrm{10}} =\left(\mathrm{1001001}.\mathrm{011010}…\right)_{\mathrm{2}} \\ $$
Commented by Rasheed.Sindhi last updated on 12/Sep/20
Thanks miss.
$$\mathcal{T}{hanks}\:{miss}. \\ $$

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