100 In Binary

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

We have different types of number systems in Math.

The binary number system is one of the most common systems to be used. This system uses only two digits \(0\) and \(1\)

Thus, the numbers in this system have a base 2

0 and 1 are called bits.

Let us find an answer to the question what is 100 in binary?

100 in binary is cartoon image

In this mini lesson, we will explore the world of \(100_{10}\) in binary. We will walk through the answers to the questions like what is meant by converting \(100_{10}\) from decimal to binary, and how to convert \(100_{10}\) from decimal to binary number.

Lesson Plan 

What Is Meant By Converting 100 From Decimal to Binary?

\(100_{10}\) is a decimal representation. Converting 100 from decimal to binary means to write or represent 100 using 2 bits only, i.e., 0 and 1.

In converting 100 in binary, we need to change the base 10 to base 2

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

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

\(100_{10}\) in binary is \(1100100_{2}\)


How to Convert 100 From Decimal to Binary Number?

Let us look at the steps showing the conversion of 100  from decimal to binary.

Let us look at the steps showing the conversion of 100 from decimal to binary.

Step-1

Identify the base of the required number. In this case, the base of 100 is 10, i.e., \(100_{10}\)

Step-2

Divide the given number 100 by the base of the required number, i.e. 2

Step-3

Note down the quotient and the remainder.

Step-4

Divide the number 100 until we get the quotient to be less than the base which is 2

Step-5

Read all the remainders including the last quotient from bottom to top.

(Note: digits marked in the green boxes represent the binary form of 100.)

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

100 in binary : - Division of 100 by 2 to convert from decimal to binary

Therefore  \(100_{10} = 1100100_2 \)

Binary to Decimal Conversion

Step 1: Identify the base of the given number.

Here, the base of \(100111_2\) is 2

Step 2: Multiply each digit of the given number, starting from the rightmost digit, with the exponents of the base.

The exponents should start with 0 and increase by 1 every time as we move from right to left.

Since the base here is 2, we multiply the digits of the given number by \(2^0, 2^1, 2^2,...\) from right to left.

number system conversion example of binary number 100111 into decimal number system

Step 3: We just simplify each of the above products and add them.

number system conversion example of the binary number 100111 into decimal number system

Here, the sum is the equivalent number in the decimal number system of the given number.

\(\therefore 100111_2 = 39_{10}\)

Decimal to Binary Converter.

Try to convert some more decimal numbers into binary using decimal to binary converter.

 
important notes to remember
Important Notes
  • In the word binary, the meaning of the initials "Bi" is two. For example, bike(\(2\) Wheels).
  • The binary system is represented by base 2. For example, \(1100100_2\).
  • The decimal system is represented by base 10. For example, \(100_{10}\).

Solved Examples 

Let us have a look at solved examples on 100 in binary to understand the difference between decimal to binary and binary to decimal conversion without using a decimal to binary converter.

Example 1

 

 

Jamie is trying her hands on number system conversion. She needs guidance in converting \(1001_2\) into the decimal system. Help Jamie with the correct steps.

Solution

For binary to decimal conversion Jamie need to follow the below steps:

Step 1: Identify the base of the given number.For example, the base of \(1001_2\) is 2 now convert it to the number with base 10

Step 2: Multiply each digit of the given number, starting from the rightmost digit, with the exponents of the base.

Step 3: The exponents should start with 0 and increase by 1 every time as we move from right to left.

Since the base here is 2, we multiply the digits of the given number by \(2^0, 2^1, 2^2,...\) from right to left.

\(1001_{2}=
1\times2^{0}=1\times 1=1\\\
0\times2^{1}=0\times 2=0\\\
0\times2^{2}=0\times 4=0\\\
1\times2^{3}=1\times 8=8\)

Step 4: Simplify each of the products and add them.

\(\begin{align}1+0+0+8 &=9\\\ 1001_{2} &=9_{10}\end{align}\)

\(\therefore\) \(1001_{2}=9_{10}\)

Example 2

 

 

Hary is trying to convert \(300_{10}\) into the binary system (base- \(2\)).What process should Hary use?

Solution

\(300_{10}\) is in the decimal system.

Hary needs to divide \(300\) by \(2\) and note down the quotient and the remainder.

I) Identify the base of the required number, ie., 2

II) Divide the given number 300 by the base of the required number, i.e, \(300 \div 2\)

III) Note down the quotient and the remainder.

IV) Divide the number 300 until we get the quotient to be less than 2

V) Read all the remainders including the last quotient from bottom to top.

Repeat this process for every quotient until we get a quotient which is less than 2

number system conversion of decimal number 300 into binary number system

\(\therefore\) \(300_{10}\) \(=\) \(100101100_2\)
Example 3

 

 

Help Ron in converting the decimal number \(76_{10}\) to system with \(1\) and \(0\) bit.

Solution

\(76_{10}\) is in the decimal system.

Ron needs to divide \(76\) by \(2\) and note down the quotient and the remainder.

I) Identify the base of the required number, ie., 2

II) Divide the given number 76 by the base of the required number, i.e, \(76 \div 2\)

III) Note down the quotient and the remainder.

IV) Divide the number 76 until we get the quotient to be less than 2

V) Read all the remainders including the last quotient from bottom to top.

Repeat this process for every quotient until we get a quotient which is less than 2

converion of 76 into binary

\(\therefore\)  \(76_{10}\) \(=\) \(1001100_2\)

Interactive Questions on 100 In Binary

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 Question
Just like in our chapter we used 0-9 numbers for decimal and 0 & 1 bits for binary. In the octal system, we use 0-7. Can you follow the same process and see if you can convert the below binary to octal.
a) \(1000_{2}\)
b) \(10_{2}\)
c) \(1100_{2}\)
d) \(1001_{2}\)

Let's Summarize

The mini-lesson targeted the fascinating concept of 100 in binary. The math journey around 100 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.


FAQ's on what is 100 in binary?

1. What is 2 in binary?

\(2_{10}\) in binary is \(10_{2}\)

2. What does 101 mean in binary?

Meaning of \(101_{10}\) in binary is \(1100101_{2}\)

3. What is base 10?

To represent 10 in a number system we are using \(1\) to \(9\) digits. Here base 10 is used as a base to represent decimal numbers. 

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