Question

The binary number 10111 is equivalent to the decimal number
A. 19
B. 31
C. 23
D. 22

Answer 1

Hint: First we will convert the given binary number into the decimal number by multiplying each digit of the given number by the corresponding power of two in a sum and then solve the powers to find the required value.

Complete step by step answer:

We are given that the binary number 10111.

We know that a binary number is a number expressed in the base 2 numeral system or binary numeral system which uses only two symbols, mainly 0 and 1.

Since we know that the a binary number into the decimal number by multiplying each digit of the number by the corresponding powers of two in a sum, that is, ones place will be multiplied by 0th power of 2, tens place will be multiplied by 1th power of 2 and so on.

Converting the given binary number into the decimal number by multiplying each digit of the given number by the corresponding power of two in a sum, we get

\[ \Rightarrow {\left( {10111} \right)_B} = 1 \times {2^4} + 0 \times {2^3} + 1 \times {2^2} + 1 \times {2^1} + 1 \times {2^0}\]

Solving the powers in the above equation, we get

\[
   \Rightarrow {\left( {10111} \right)_B} = 16 + 0 + 4 + 2 + 1 \\
   \Rightarrow {\left( {10111} \right)_B} = 23 \\
 \]

Thus, the required decimal number is 23.

Hence, option C is correct.

Note: In solving these types of questions, the key concept is to change any given binary number, we have to just apply the formula. And according to that, to convert the number before the decimal point we had to start from the rightmost digit before the point and multiply each digit by \[{2^n}\] where \[n\] will be the position of the digit starting from 0 and then add them up.