Question

Convert \[{{\left( 127 \right)}_{10}}\] into binary system 107?

Answer 1

Hint: We have to convert the given number into binary form. As we can see the base is given as 10 so we can say that the given number is in decimal form. So to convert from decimal form to binary we have to divide the number with 2 and take its remainder to form a binary number.

Complete step-by-step answer:
Let us know the numerical forms and their bases.
Decimal -10
Binary -2
Octal-8
Hexadecimal-16
Now we will see some conversion methods to convert from one number system to another number system.
To convert from decimal to binary we have to divide the number by 2.
To convert from decimal to octal we have to divide the number by 8.
To convert from decimal to hexadecimal we have to divide the number by 16.
Likewise we can convert from one number system to another.
Now the given expression is
\[{{\left( 127 \right)}_{10}}\]
We can see that It is given as base 10. So we can say from the above learnings it will belong to decimal form. Now we have to convert from decimal to binary.
As discussed above we have to divide the number by 2.we have to take the remainder at every step to form the binary number.
Given number is \[127\]
We have to divide the number by 2 and we have to take the remainder.
So dividing the number look like
\[\begin{align}
  & 2\left| \!{\underline {\,
  127 \,}} \right. \\
 & 2\left| \!{\underline {\,
  63-1 \,}} \right. \\
 & 2\left| \!{\underline {\,
  31-1 \,}} \right. \\
 & 2\left| \!{\underline {\,
  15-1 \,}} \right. \\
 & 2\left| \!{\underline {\,
  7-1 \,}} \right. \\
 & 2\left| \!{\underline {\,
  3-1 \,}} \right. \\
 & 1-1 \\
\end{align}\]

We can see that remainder at every stage is 1. we will combine all the remainders to get the binary form.
So we have 7 one’s in the remainder. so our binary form will look like
\[1111111\]
\[{{\left( 127 \right)}_{10}}=1111111\]

Note: We can also convert the number from binary to decimal form. We can take values of power of 2 at each position in the binary form. So by using conversions we can convert from any number system to other and vice versa.