Question

Convert decimal to octal numbers.

1.) (4507) to the power 10=(?) to the power 8

2.) (7606) to the power 10=(?) to the power 8


3.) (7757) to the power 10=(?) to the power 8

please solve it step by step if not possible in this app then do it in your copy please I am requesting you and don't write rubbish things...........​

Answer 1

To convert a decimal number to octal, first we convert the given number to its binary equivalent and then it is converted to octal.

→   To convert a decimal number to its binary equivalent -

1.  Divide the given number continuously by 2, until the number becomes 0.

2. The remainder obtained on each division should be noted from top to bottom as the division proceeds.

3. The binary equivalent is obtained by writing the remainders in the order from bottom to top.

→   To convert a binary number to its octal equivalent -

1.  Make groups of consecutive three digits among the number from right to left.

2. Replace each group by its octal equivalent as follows:

$\begin{aligned}\sf{(000)_2=(0)_8}\quad\quad&\quad\quad \sf{(001)_2=(1)_8}\\\\\sf{(010)_8=(2)_8\quad\quad&\quad\quad\sf{(011)_2=(3)_8}}\\\\\sf{(100)_2=(4)_8\quad\quad&\quad\quad\sf{(101)_2=(5)_8}}\\\\\sf{(110)_2=(6)_8}\quad\quad&\quad\quad\sf{(111)_2=(7)_8}\end{aligned}$

(1)  Converting $\sf{(4507)_{10}}$ to binary,

$\begin{tabular}{r|lc}\sf{2}&\sf{4507}&\\\cline{2-}\sf{2}&\sf{2253}&\sf{1}\\\cline{2-}\sf{2}&\sf{1126}&\sf{1}\\\cline{2-}\sf{2}&\sf{563}&\sf{0}\\\cline{2-}\sf{2}&\sf{281}&\sf{1}\\\cline{2-}\sf{2}&\sf{140}&\sf{1}\\\cline{2-}\sf{2}&\sf{70}&\sf{0}\\\cline{2-}\sf{2}&\sf{35}&\sf{0}\\\cline{2-}\sf{2}&\sf{17}&\sf{1}\\\cline{2-}\sf{2}&\sf{8}&\sf{1}\\\cline{2-}\sf{2}&\sf{4}&\sf{0}\\\cline{2-}\sf{2}&\sf{2}&\sf{0}\\\cline{2-}\sf{2}&\sf{1}&\sf{0}\\\cline{2-}\sf{2}&\sf{0}&\sf{1}\\\cline{2-}\end{tabular}$

Hence, $\sf{(4507)_{10}=(1000110011011)_2}$

Converting the binary number to octal,

$\longrightarrow\sf{(001,000,110,011,011)_2=(10633)_8}$

Therefore, $\sf{\underline{\underline{(4507)_{10}=(10633)_8}}}$

(2)  Converting $\sf{(7606)_{10}}$ to binary,

$\begin{tabular}{r|lc}\sf{2}&\sf{7606}&\\\cline{2-}\sf{2}&\sf{3803}&\sf{0}\\\cline{2-}\sf{2}&\sf{1901}&\sf{1}\\\cline{2-}\sf{2}&\sf{950}&\sf{1}\\\cline{2-}\sf{2}&\sf{475}&\sf{0}\\\cline{2-}\sf{2}&\sf{237}&\sf{1}\\\cline{2-}\sf{2}&\sf{118}&\sf{1}\\\cline{2-}\sf{2}&\sf{59}&\sf{0}\\\cline{2-}\sf{2}&\sf{29}&\sf{1}\\\cline{2-}\sf{2}&\sf{14}&\sf{1}\\\cline{2-}\sf{2}&\sf{7}&\sf{0}\\\cline{2-}\sf{2}&\sf{3}&\sf{1}\\\cline{2-}\sf{2}&\sf{1}&\sf{1}\\\cline{2-}\sf{2}&\sf{0}&\sf{1}\\\cline{2-}\end{tabular}$

Hence, $\sf{(7606)_{10}=(1110110110110)_2}$

Converting the binary number to octal,

$\longrightarrow\sf{(001,110,110,110,110)_2=(16666)_8}$

Therefore, $\sf{\underline{\underline{(7606)_{10}=(16666)_8}}}$

(3) Converting $\sf{(7757)_{10}}$ to binary,

$\begin{tabular}{r|lc}\sf{2}&\sf{7757}&\\\cline{2-}\sf{2}&\sf{3878}&\sf{1}\\\cline{2-}\sf{2}&\sf{1939}&\sf{0}\\\cline{2-}\sf{2}&\sf{969}&\sf{1}\\\cline{2-}\sf{2}&\sf{484}&\sf{1}\\\cline{2-}\sf{2}&\sf{242}&\sf{0}\\\cline{2-}\sf{2}&\sf{121}&\sf{0}\\\cline{2-}\sf{2}&\sf{60}&\sf{1}\\\cline{2-}\sf{2}&\sf{30}&\sf{0}\\\cline{2-}\sf{2}&\sf{15}&\sf{0}\\\cline{2-}\sf{2}&\sf{7}&\sf{1}\\\cline{2-}\sf{2}&\sf{3}&\sf{1}\\\cline{2-}\sf{2}&\sf{1}&\sf{1}\\\cline{2-}\sf{2}&\sf{0}&\sf{1}\\\cline{2-}\end{tabular}$

Hence, $\sf{(7757)_{10}=(1111001001101)_2}$

Converting the binary number into octal,

$\longrightarrow\sf{(001,111,001,001,101)_2=(17115)_8}$

Therefore, $\sf{\underline{\underline{(7757)_{10}=(17115)_8}}}$