Answer
412.8k+ views
Hint: The binary numbers are expressed in the base-2 numeral system. Sum of two binary numbers can be obtained adding one number to another number and get an answer. We need to remember the rules for the addition of binary numbers.
Complete step by step solution:
We know that the binary numbers are positional numeral systems employing 2 as the base and so requiring only two different symbols for its digits 0 and 1, instead of usual to different symbols needed in a decimal system. 0 and 1 are known as binary digits. Now, we have to find the sum of given numbers those are ${{\left( 1000010 \right)}_{2}}\text{and} {{\left( 11011 \right)}_{2}}$. We have to convert these binary numbers into the decimal system. For the first number, its decimal number can be given by ${{\left( 1000010 \right)}_{2}}$.
Now count these numbers one by one from right side, we get,
$\begin{align}
& {{\left( 1000010 \right)}_{2}} \\
& \downarrow \downarrow \downarrow \downarrow \downarrow \downarrow \downarrow \\
& 6543210 \\
\end{align}$
As there is base of 2.
$\begin{align}
& {{2}^{6}}+{{2}^{1}}=64+2 \\
& ={{\left( 66 \right)}_{10}} \\
\end{align}$
So, ${{\left( 1000010 \right)}_{2}}={{\left( 66 \right)}_{10}}$ in decimal system for second number, its decimal number can be given by,
${{\left( 11011 \right)}_{2}}$ Similarly we get,
$\begin{align}
& {{2}^{5}}+{{2}^{4}}+{{2}^{1}}+{{2}^{0}} \\
& =32+16+2+1 \\
& ={{(61)}_{10}} \\
\end{align}$
Therefore, ${{\left( 110011 \right)}_{2}}={{\left( 61 \right)}_{10}}$ in decimal system we have to add the decimal form of two numbers
${{\left( 66 \right)}_{10}}+{{\left( 61 \right)}_{10}}={{\left( 127 \right)}_{10}}$
Now, solve the L.C.M of 127
It is clear that the final answer will contain the 6 digits.
${{\left( 127 \right)}_{10}}={{\left( 111111 \right)}_{2}}$
${{\left( 111111 \right)}_{2}}$ Is the binary form of ${{(127)}_{10}}$
So the correct option is (b).
Additional information:
Modern day computers use binary numbers to operate- this is the fact well known to people studying computer science or to those using these machines on more than frequent basis.
Note:
There are three basic rules for adding binary numbers. It is advised to remember those rules in digital electronics; a binary number is expressed in the base- 2 numeral system which uses only two symbols: typically 0 and 1 the base – 2 numeral system is a positional notation with the radix 2.
Complete step by step solution:
We know that the binary numbers are positional numeral systems employing 2 as the base and so requiring only two different symbols for its digits 0 and 1, instead of usual to different symbols needed in a decimal system. 0 and 1 are known as binary digits. Now, we have to find the sum of given numbers those are ${{\left( 1000010 \right)}_{2}}\text{and} {{\left( 11011 \right)}_{2}}$. We have to convert these binary numbers into the decimal system. For the first number, its decimal number can be given by ${{\left( 1000010 \right)}_{2}}$.
Now count these numbers one by one from right side, we get,
$\begin{align}
& {{\left( 1000010 \right)}_{2}} \\
& \downarrow \downarrow \downarrow \downarrow \downarrow \downarrow \downarrow \\
& 6543210 \\
\end{align}$
As there is base of 2.
$\begin{align}
& {{2}^{6}}+{{2}^{1}}=64+2 \\
& ={{\left( 66 \right)}_{10}} \\
\end{align}$
So, ${{\left( 1000010 \right)}_{2}}={{\left( 66 \right)}_{10}}$ in decimal system for second number, its decimal number can be given by,
${{\left( 11011 \right)}_{2}}$ Similarly we get,
$\begin{align}
& {{2}^{5}}+{{2}^{4}}+{{2}^{1}}+{{2}^{0}} \\
& =32+16+2+1 \\
& ={{(61)}_{10}} \\
\end{align}$
Therefore, ${{\left( 110011 \right)}_{2}}={{\left( 61 \right)}_{10}}$ in decimal system we have to add the decimal form of two numbers
${{\left( 66 \right)}_{10}}+{{\left( 61 \right)}_{10}}={{\left( 127 \right)}_{10}}$
Now, solve the L.C.M of 127
![seo images](https://www.vedantu.com/question-sets/e75163f1-c7f7-4847-9486-9e379664a94f7296289740794674141.png)
It is clear that the final answer will contain the 6 digits.
${{\left( 127 \right)}_{10}}={{\left( 111111 \right)}_{2}}$
${{\left( 111111 \right)}_{2}}$ Is the binary form of ${{(127)}_{10}}$
So the correct option is (b).
Additional information:
Modern day computers use binary numbers to operate- this is the fact well known to people studying computer science or to those using these machines on more than frequent basis.
Note:
There are three basic rules for adding binary numbers. It is advised to remember those rules in digital electronics; a binary number is expressed in the base- 2 numeral system which uses only two symbols: typically 0 and 1 the base – 2 numeral system is a positional notation with the radix 2.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Select the word that is correctly spelled a Twelveth class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What organs are located on the left side of your body class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)