32 in Binary

In this mini-lesson, we will learn about writing 32 in binary system along with examples.

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."

Then what is a binary system? Well, it is a system in which data that is inputted into a computer is converted into 0s and 1s, irrespective of the type of data. In other words, pictures, videos, movies, and cartoons in the eyes of a computer are just 0s and 1s.

Here are some interesting features about the binary system:

  • Thus the numbers in this system have a base 2
  • 0 and 1 are called bits.
  • 8 bits together make a byte.
  • The data in computers is stored in terms of bits and bytes.

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

Lesson Plan 

What is 32 as a Binary Number?

Here, 32 has no base. So by default, its base is 10

We have to convert it into binary system. i.e., we have to convert 32 into a number that is made up of the digits 0 and 1

32 in binary system is:

32 (or) \(32_{10} = 100000_2\)

But how to express 32 in binary? Let's learn.

 
important notes to remember
Important Notes
  1. To convert a number from binary system to decimal system:

    Multiply each digit of the given number, starting from the rightmost digit, with the exponents of 2, where the exponents start from \(0\) and increase by \(1\) every time. Then just add the above products.

  2. To convert a number from the decimal system to the binary system:

    Divide the given number by 2 and note down the quotient and the remainder in the “quotient-remainder” form repetitively until we get the quotient to be less than the base. The given number in the decimal number system is obtained just by reading all the remainders and the last quotient from bottom to top.

How to convert 32 in binary form?

To convert 32 into binary, we have to divide 32 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.

How to convert 32 in binary form?

32 in binary system is obtained by just by reading all the remainders and the last quotient from bottom to top.

How to convert 32 in binary form?

Thus 32 in binary is: 

32 (or) \(32_{10} = 100000_2\)

Solved Examples

Example 1

 

 

Sophia understood that 32 in binary form is 1000002. But she would like to cross-check her answer. How can she do that?

Solution

Sophia tried to convert 1000002 into the decimal system.

She recalled the fact that to convert a number from binary system to decimal system we have to:

multiply each digit of the given number, starting from the rightmost digit, with the exponents of 2, where the exponents start from \(0\) and increase by \(1\) every time. Then we just add the above products.

10000 from binary to decimal: the answer is 32

Wow! 32 is back!

This way, Sophia can verify her answer.
Example 2

 

 

Can we help Jake convert 171 (or) \(171_{10}\) into the binary system?

Solution

We do it just by using the same procedure of converting 32 in binary form.

171 from base 10 to binary (base 2)

\(\therefore\) \(171_{10}=10101011_2\)

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.

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Challenge your math skills
Challenging Questions

In this lesson, we have learned how to convert base 32 in binary. Can you now try to convert the following numbers as instructed?

  1. Convert \(101010_2\) into the decimal system.
  2. Convert 1000 into the binary system.

Let's Summarize

The mini-lesson targeted the fascinating concept of 32 in binary. The math journey around 32 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 not only it is relatable and easy to grasp, but also will 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.


FAQs on 32 in Binary

1. What is the binary of 32?

We have already seen that the binary form of 32 is 100000\(_2\).

2. How do you write 14 in binary?

By the procedure that we learned from this page, 14 in binary system is 1110\(_2\). i.e.,

14 = 1110\(_2\).

3. What is the binary equivalent of 51?

By the procedure that we learned from this page, 51 in binary system is 110011\(_2\). i.e.,

51=110011\(_2\).

4. What does 11111111 in binary mean?

By the procedure that we learned from this page, we can see that 11111111 in binary means 255 in decimal system. i.e.,

11111111\(_2\)=255\(_{10}\).

5. What does 101 in binary mean?

By the procedure that we learned from this page, 101 in the binary system means 5 in the decimal system.

101\(_2\)=5\(_{10}\).

6. How do you write 256 in binary?

By the procedure that we learned from this page, 256 in the binary system is 100000000\(_2\). i.e.,

256 = 100000000\(_2\).

7. What is the binary for 255?

By the procedure that we learned from this page, 255 in binary system is 11111111\(_2\). i.e.,

255 = 11111111\(_2\).

8. What does 01011 in binary mean?

By the procedure that we learned from this page, we can see that 01011 in binary means 11 in the decimal system. i.e.,

01011\(_2\)=11\(_{10}\).

9. How do you write 7 in binary?

By the procedure that we learned from this page, 7 in binary system is 111\(_2\). i.e.,

7 = 111\(_2\).

10. What is the binary of 100?

By the procedure that we learned from this page, 100 in the binary system is 1100100\(_2\). i.e.,

100 = 1100100\(_2\).

  
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