15 In Binary

In this mini-lesson, we will learn about writing 15 in binary along with examples.

Language is a medium to communicate with each other or to express our feelings. Even computers have their own language. Computers understand only 0's and 1's. They are called bits. A computer always works with numbers. Be it a word, image, audio, or video, everything is converted into 0's and 1's. 

In math, we follow a standard system to represent numbers. We call it the number system.

We have four different types of number systems with different bases. We can write any digit in any of these number systems.

Number systems chart showing binary number system, base 10 number system, octal number system, decimal number system, and hexadecimal number system.

Let us learn how to write 15 in binary on this page.

Lesson Plan 

What Is Meant by Converting 15 From Decimal to Binary?

In our daily life, we represent numbers using the digits 0, 1, 2, ..., 9. This system where we use the digits 0, 1, 2, ..., 9 to write numbers is called the "decimal system."

Though we do not write any base to the numbers we write in our daily life, the default base is 10. That is, we follow the base 10 number system.

decimal number system has a base 2 and uses 0-9

Binary number system has a base 2 and uses only 0 and 1, base 10 number system

Therefore, 15 can also be written as \(15_{10}\) in a decimal representation.

Converting 15 from decimal to binary means to write or represent 15 using 2 bits only, i.e., 0 and 1 because the base-2 number system uses only 2 digits (0 and 1).

\(15_{10}\) in binary is \(1111_{2}\).


How to Convert 15 From Decimal to Binary Number? 

Here, 15 has no base. So by default, its base is 10

The base of the binary system is 2

So we have to convert \(15_{10}\) to a number with base 2 say \(X_{2}\).

To convert 15 into binary, we have to divide 15 by 2 and note down the quotient and the remainder in the “quotient-remainder” form.

Repeat this process (dividing the quotient again by 2) until we get the quotient to be less than the base.

 15 in binary

15 in the binary system is obtained just by noting down all the remainders and the last quotient from bottom to top.

what is 15 in binary

Thus, 15 in binary is:

15 (or) \(15_{10}\) = \(1111_{2}\)

You can convert any number in a decimal system to a binary-based number using the following calculator:

 
important notes to remember
Important Notes
  • Sometimes the base is also referred to as "Radix."
  • Base-2 number system uses only 2 digits (0 and 1), base-8 number system uses 8 digits (0-7), base-10 number system uses digits from (0-9), and base-10 number system uses digits from (0-9) and alphabets (A-F).

Solved Examples

Example 1

 

 

Charlie is entering the number 13 on a computer. How will the computer convert it into binary and store it? 

Solution

To convert 13 into binary, the computer follows the given steps:

Step 1: Divide 13 by 2 to find the quotient and remainder.

Step 2: Divide the quotient obtained again by 2

Step 3: Repeat the process until the quotient becomes lesser than 2

what is 13 in binary

\( \therefore \) 13 in binary  = \(1101_2  \)
Example 2

 

 

Trevor wants to write his age in binary. He is 18 years old. Can you help him write his age in binary?

Solution

18 can be converted into binary following the given steps:

Step 1: Divide 18 by 2 to find the quotient and remainder.

Step 2: Divide the quotient obtained again by 2.

Step 3: Repeat the process until the quotient becomes lesser than 2

what is 18 in binary

\(\therefore \text { Age of Trevor in binary } =10010 _2 \) 
Challenge your math skills
Challenging Questions

In this lesson, we have learned how to convert 15 in binary. Can you now try to convert the following binary numbers into corresponding numbers with decimal bases?

  1. \(10100_2\)
  2. \(10000_2\)
  3. \(11011_2\)

Interactive Questions

Here are a few activities for you to practice. 

Select/type your answer and click the "Check Answer" button to see the result.

 
 
 
 

Let's Summarize

The mini-lesson targeted the fascinating concept of writing 15 in binary. The math journey around the number 15 in binary starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that is not only relatable and easy to grasp but will also stay with them forever. Here lies the magic with Cuemath.

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.


Frequently Asked Questions (FAQs)

1. What is the binary number of 15?

15 in binary written as 11112

2. How do you write 7 in binary?  

7 in binary is written as 1112 

3. How do you read binary? 

Reading binary code means converting the binary number into the decimal number system so that it can be easily understood as we are more familiar with this number system.

Hence, \(111_2\) will be read as 7 since it is the decimal system equivalent of \(111_2\)

More Important Topics
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