Question

Convert $(146){}_{10}$ to base $2$
$A)$ ${(1010010)_2}$
$B)$ ${(100010010)_2}$
$C)$ ${(10010010)_2}$
$D)$ ${(10001010)_2}$

Answer 1

Hint: First we have to define what the terms we need to solve the problem are.
The provided problem is based on the binary system. Then a long process is the decimal to binary conversion, usually achieved by splitting the decimal number into two. Numerical values are represented by two different symbols; zero, one knowing the process of division to answer these questions.

Complete step-by-step solution:
According, to convert any given decimal number into its equivalent binary number system.
Binary numbers are representing as base $2$, octal numbers are representing as base $8$
Decimal numbers are representing as base $10$ and hexadecimal numbers is representing as base $16$
Decimal to binary conversion is a long process which is usually done by dividing the decimal number to 2
Continuous division of integers is carried out until the remainder reaches 0 or 1.
We represent the $(146){}_{10}$ to base $2$, since we know that the binary number is represent by base 2
Let us begin with dividing $\dfrac{{146}}{2}$ so we will get remainder as zero and quotient as $73$
Again, division by 2 we get $\dfrac{{73}}{2}$ but in here we get remainder as one and quotient as \[36\]
Similarly, we approach the same thing further we get $\dfrac{{36}}{2}$ quotient as $18$ and remainder zero
And $\dfrac{{18}}{2}$ quotient as $9$ and remainder zero, $\dfrac{9}{2}$ quotient as $4$ and remainder one
$\dfrac{4}{4}$ quotient as $2$ and remainder zero and finally $\dfrac{2}{2}$ quotient as one and remainder zero
Therefore, writing the remainders in reverse order that is from bottom to top we get ${(10010010)_2}$
As we clearly see from bottom to top the remainders are $1,0,0,1,0,0,1,0$ so no other option is possible except option C.

Note: It is possible to solve the above problem using the binary system formula, the numbers can be positioned to the left or the right of the point and its direct implementation in electronic circuits too.