Question

A number in the binary system is 110001. It is equal to which of the following numbers in the decimal system?
A. $45$
B. $46$
C. $48$
D. $49$

Answer 1

Hint: According to the question we have to convert the given binary system into the decimal system. So, first of all we have to understand about the binary system which is as explained below:
Binary system: The binary system is one of the four types of system in the computer application where binary numbers are represented only by the two numbers as 0 and 1 and binary numbers here are expressed in base 2 numeral system.
So, first of all to convert the given binary system into decimal we have to use the formula as mentioned below:

Formula used: Decimal$ = {d_0} \times {2^0} + {d_1} \times {2^1} + {d_2} \times {2^2} + ............$ ………..(A)
Where, ${d_0},{d_1}.........$ are the digits of the given binary number.

Complete step-by-step solution:
Step 1: First of all we have to understand about the binary system which is already explained in the solution hint.
Step 2: Now, we have to use the formula (A) as mentioned in the solution hint to determine the decimal of the given binary numbers.
$ \Rightarrow 1 \times {2^0} + 0 \times {2^1} + 0 \times {2^2} + 0 \times {2^3} + 1 \times {2^4} + 1 \times {2^5}$…………(2)
Step 3: Now, we have to solve the expression (2) as obtained in the solution step 2. Hence,
$
   = 1 + 0 + 0 + 0 + 16 + 32 \\
   = 49
 $
Final solution: Hence, with the help of (A) we find the decimal number of the given binary system that is $49$.

Therefore option (D) is correct.

Note: Decimal number system is represented by its base. If the base is 2 it is a binary number, if the base is 10, then it is called a decimal number system.
The binary system is one of the four types of system in the computer application where binary numbers are represented only by the two numbers as 0 and 1.