Question

Decimal number $15$ is equivalent to the binary number:
A. $110001$
B. $000101$
C. $101101$
D. $001111$

Answer 1

Hint:We will solve step by step to convert the decimal number $15$ into the binary number. As we know that, in the decimal number we use $10$ digits and in the binary number we use only $2$ digits. Therefore, we will divide the decimal number by $2$ to convert it into the binary number. Here, the quotient obtained by dividing the number will consist of two parts, that is, the whole part and the fractional part which is also known as remainder. Here, we will keep the fractional part aside and the whole part will be used for another step.

Complete step by step answer:
The steps used to convert the decimal number $15$ into the binary digit is given below.
1. Firstly, we will divide $15$ by $2$ to get the quotient. Here, we will keep the whole part of the quotient for the next step and set the remainder aside as shown below
$15 \div 2 = 7$ with the remainder $1$
2. Now, we will divide $7$ by $2$ to get the quotient as shown below
$7 \div 2 = 3$ with the remainder $1$
3. Now, we will divide $3$ by $2$ to get the quotient, as shown below
$3 \div 2 = 1$ with the remainder $1$
4. Now, we divide $1$ by $2$ to get the quotient, as shown below
$1 \div 2 = 0$ with the remainder $1$
Now, we will combine the remainders obtained in the reverse order to get the answer.Therefore, the decimal number $15$ is equivalent to the binary number is $001111$.

Hence, option D is the correct answer.

Note:Here you might think that the answer obtained was $1111$ but the answer we have provided is $001111$. This is because it is because it is said that if the answer obtained will be four digits then we will add two zero in the first place of the digit obtained. That is why we have got the answer as $001111$.