255 in Binary

255 in Binary

In this mini-lesson, we will learn about writing 255 in a 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? Here are some facts about the binary system.

  • The binary number system uses only two digits: 0 and 1
  • 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 255 as a Binary Number?

Here, 255 has no base. So by default, its base is 10

We have to convert it into a binary system. i.e., we have to convert 255 into a number that is made up of the digits 0 and 1

255 in the binary system is,

255 (or) 255\(_{10}\) = 11111111\(_{2}\)

But how to express 255 in binary? Let's learn.

 
important notes to remember
Important Notes
  1. To convert a number from binary system to the 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 decimal system to a 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 255 in binary form?

To convert 255 into binary, we have to divide 255 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 255 in binary form?

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

How to convert 255 in binary form?

Thus 255 in binary is: 

255 (or) 255\(_{10}\) = 11111111\(_{2}\)

Solved Examples

Example 1

 

 

Jim understood that 255 in binary form is 11111111\(_{2}\). But he would like to cross-check her answer. How can he do that? 

Solution

Jim tried to convert 11111111\(_{2}\) into the decimal system.

He recalled the fact that to convert a number from binary system to the 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.

11111111 from binary to decimal: the answer is 25

Hurray! 255 is back!

It means Jim's answer is correct.

This way, Jim can verify his answer.
Example 2

 

 

Can we help Jake convert 129 (or) 129\(_{10}\) into the binary system?

Solution

We do it just by using the same procedure of converting 255 in binary form.

129 from base 10 to binary (base 2)

\(\therefore\) \(129_{10}=10000001_2\)

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.

 
 
 
 
 
Challenge your math skills
Challenging Questions

In this lesson, we have learned how to convert base 255 into binary. Can you now try to convert the following numbers as instructed?

  1. Convert 10101101\(_{2}\) into the decimal system.
  2. Convert 1001 into the binary system.

Let's Summarize

The mini-lesson targeted the fascinating concept of 255 in binary. The math journey around 255 in binary started with what a student already knew and went 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. 

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 255 in Binary

1. How do you multiply binary numbers?

To multiply two binary numbers, the easiest method is:

  • Convert both of them into the decimal system.
  • Multiply them and find the product.
  • Convert the product back into the binary system to have the answer in the binary form.

2. What is the binary value of 255?

As we learned on this page, the binary value of 255 is 11111111\(_{2}\).

3. How do you write 7 in binary?

By the procedure that we learned from this page, 7 in the binary system is 111\(_{2}\). i.e.,

7 = 111\(_{2}\).

4. How do you write 200 in binary?

By the procedure that we learned from this page, 200 in the binary system is 11001000\(_{2}\). i.e.,

200 = 11001000\(_{2}\).

5. What is the binary number for 240?

By the procedure that we learned from this page, 240 in the binary system is 11110000\(_{2}\). i.e.,

240 = 11110000\(_{2}\).

6. How do you write 16 in binary?

By the procedure that we learned from this page, 16 in the binary system is 10000\(_{2}\). i.e.,

16 = 10000\(_{2}\).

7. How do you write 192 in binary?

By the procedure that we learned from this page, 192 in the binary system is 11000000\(_{2}\). i.e.,

192 = 11000000\(_{2}\).

8. How do you write 63 in binary?

By the procedure that we learned from this page, 63 in the binary system is 111111\(_{2}\). i.e.,

63 = 111111\(_{2}\).

9. What is the binary number for 250?

By the procedure that we learned from this page, 250 in the binary system is 11111010\(_{2}\). i.e.,

250 = 11111010\(_{2}\).

10. What is the binary number for 256?

By the procedure that we learned from this page, 256 in the binary system is 100000000\(_{2}\). i.e.,

256 = 100000000\(_{2}\).

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