21 in Binary
2026-02-28 17:46 Diff
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Last updated on September 30, 2025

The binary system is a type of numerical system that we use to represent numbers with two digits: 0 and 1. The number 21 in binary is represented as 10101. It is a system of numerical data that computers use, as they operate with electric signals. In this topic, we are going to talk about 21 in binary.

21 in Binary Conversion

To get the binary number of 21, we need to divide 21 by 2 and record the remainder. It is done as below:

21 / 2 → quotient = 10, remainder = 1

10 / 2 → quotient = 5, remainder = 0

5 / 2 → quotient = 2, remainder = 1

2 / 2 → quotient = 1, remainder = 0

1 / 2 → quotient = 0, remainder = 1

Finally, we read the remainders from bottom to top and we get 10101 which is the binary number of 21.

21 in Binary Chart

To understand the binary of 21 let us look at the binary chart of numbers from 20 to 30:

Numericals Binary 20 00010100 21 00010101 22 00010110 23 00010111 24 00011000 25 00011001 26 00011010 27 00011011 28 00011100 29 00011101 30 00011110

In the above chart, we see the binary conversions of numbers from 20 to 30. The above chart uses 8-bit notations for the binary numbers.  We can represent the binary of 21 as 10101 or 00010101.

How to Write 21 in Binary?

We can write 21 in binary in two ways. We convert a decimal number to binary using the following two methods:

Expansion Method:

We use this method to break the number into sums of powers of 2

Step 1: Identify the largest power of 2 that fits into 21 

List powers of 2 (starting from the largest power ≤ 21):

24 = 16
23 = 8
22 = 4
21 = 2
20 = 1

Step 2: Now we find the largest power of 2 and break it down
21 = 16 + 4 + 1
This corresponds with the powers of 2:

24 = 16
22 = 4
20 = 1

Step 3: Let us write the binary number:

Place 1 in positions where the power of 2 is used
Place 0 in positions where it is not used
Arrange the powers from highest to lowest: 

24 23 22 21 20 = 10101

The final binary form is 10101

Grouping Method:

In this method we divide the number by 2, then we record the quotient, and read the remainders from bottom to top. 

Step 1: First, we have to divide 21 by 2 and record the quotient and remainder

21/2 = 10 remainder = 1

Record the remainder: 1

Step 2: Divide the previous quotient (10) by 2 

10 / 2 = 5 Remainder = 0

Record the remainder: 0

Step 3: Divide quotient 5 by 2
5 / 2 = 2 remainder = 1 
Record the remainder: 1

Step 4: Divide the previous quotient by 2

2 / 2 = 1 Remainder = 0

Record the remainder: 0

Step 5: Divide 1 by 2

1 / 2 = 0 remainder = 1

Record the remainder: 1

Now we read the remainder from bottom to top:

So 21 in binary = 10101

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Rules for Binary Conversion of 21

When converting 21 into binary, there are certain rules that must be followed. Some of the rules are as follows:

  • Rule 1: Place Value Method
     
  • Rule 2: Division by 2 Method
     
  • Rule 3: Representation Method
     
  • Rule 4: Limitation Rule

Rule 1: Place Value Method

In this method we break down the number into a sum of powers of 2, in which each of them is represented by 1 in the corresponding binary position.

  • Write the place values for binary (1, 2, 4, 8, 16, etc.)
  • Determine how 21 can be represented using a combination of these place values.
  • Assign 1 where the value is used for 21 and 0 where it does not.
  • Arrange the binary digits in sequence from left to right.

Rule 2: Division by 2 

This method converts decimal numbers into binary numbers by repeatedly dividing by 2 and then we record the remainder.

  • Divide the number by 2 and then record the remainder as 0 or 1.
  • Repeat the process of dividing the quotients by 2 until the quotient is 0.
  • Then, read the binary numbers from bottom to top.

Rule 3: Representation Method

We use the representation method to convert a binary number to its decimal equivalent using positional values.

  • A power of 2 is represented by each digit in the binary number, starting with the rightmost digit.
  • Multiply each digit with its corresponding power of 2.
  • Sum all the results you get to get the decimal equivalent.

Rule 4: Limitation Rule

The limitation rule outlines the constraints when converting between binary and decimal systems.

  • Binary representation can only be done using digits like 0 and 1.
  • It must be made sure that the conversion accurately reflects the positional values.
  • Make sure that no information is misinterpreted.

Tips and Tricks for Binary Numbers till 21

Binary is very easy to learn, but it can be quite confusing for students. Here are a few tips and tricks that students can use to master binary numbers:

  • Divide and read: Divide the number by 2 and then write down the remainders in order. We then read the remainders from bottom to top for the correct binary numbers.
  • Understanding the base-2 system: Just make sure to remember the base-2 system is the number system that uses only 2 digits (1 and 0). 
  • Memorize certain binary numbers: Memorizing binary numbers can speed up conversions. 
    1 = 1, 2 = 10, 3 = 11, 10 = 1010, 20 = 10100.

Common Mistakes and How to Avoid Them in 21 Binary Conversion

When learning about binary numbers, students might often make mistakes during conversions. Here are some common mistakes that students make and ways to avoid them:

Problem 1

Convert 13 to binary

Okay, lets begin

1101

Explanation

Divide 13 by 2 → Quotient = 6, Remainder = 1

Divide 6 by 2 → Quotient = 3, Remainder = 0

Divide 3 by 2 → Quotient = 1, Remainder = 1

Divide 1 by 2 → Quotient = 0, Remainder = 1

Read remainders from bottom to top → 1101

Well explained 👍

Problem 2

Convert 19 to binary using place value method

Okay, lets begin

10011

Explanation

Identify the powers of 2 that sum to 19:

16+2+1=19

Assign 1 to the used powers and 0 to the unused ones:

24 = 16 = 1

23 = 8 =  0

22 = 4 = 0

21 = 2 = 1

20 = 1 = 1

Arrange in order: 10011

Well explained 👍

Problem 3

Convert 45 to binary by division by 2 method

Okay, lets begin

101101

Explanation

Divide 45 by 2 → Quotient = 22, Remainder = 1

Divide 22 by 2 → Quotient = 11, Remainder = 0

Divide 11 by 2 → Quotient = 5, Remainder = 1

Divide 5 by 2 → Quotient = 2, Remainder = 1

Divide 2 by 2 → Quotient = 1, Remainder = 0

Divide 1 by 2 → Quotient = 0, Remainder = 1

Read from bottom to top: 101101
 

Well explained 👍

Problem 4

Convert 58 to binary

Okay, lets begin

111010

Explanation

Break 58 into binary place values:

32 + 16 + 8 + 2 = 58

Assign 1 only to the used values, and put 0 for the unused values.

The binary is: 111010

Well explained 👍

Problem 5

Convert 100 to binary

Okay, lets begin

1100100

Explanation

Divide 100 by 2 → Quotient = 50, Remainder = 0

Divide 50 by 2 → Quotient = 25, Remainder = 0

Divide 25 by 2 → Quotient = 12, Remainder = 1

Divide 12 by 2 → Quotient = 6, Remainder = 0

Divide 6 by 2 → Quotient = 3, Remainder = 0

Divide 3 by 2 → Quotient = 1, Remainder = 1

Divide 1 by 2 → Quotient = 0, Remainder = 1

Read the remainders from bottom to top = 1100100

Well explained 👍

FAQs on 21 in Binary

1.What is 21 in the binary number system?

2.What is 21 in 8-bit binary?

In 8-bit binary we represent 21 as 00010101. Zeroes are added in the lead for 8-bit representations.

3.Where is binary used in the real-world?

We use binary, especially in computers as they use the binary number system to store data.

4.What if we add 1 to 10101 in binary?

If we add 1 to 10101, we get 10110, which is the binary number for 22.

5.What is 2 × 10101 (21)

So 10101 = 21,

So we multiply 21 × 2 = 42

42 in binary is: 101010.

Important Glossaries for 21 in Binary

  • Binary system: It is a base-2 system that uses only two digits, 0 and 1.
  • 8-bit Representation: A way of representing numbers in binary using 8 binary digits.
  • Place value: Place value is the position of a digit in a number. This position determines the value of the number.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.