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110 LearnersLast updated on September 25, 2025
21 in Binary
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
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:
Mistake 1
Reading the remainders incorrectly
Students often read the remainders from top to bottom instead of bottom to top. This will lead to an incorrect binary number. Students must make sure that they read from bottom to top.
Mistake 2
Skipping 0s when representing binary numbers
Some students might skip 0 as they may assume that 0 has no value and write only 1s. This will lead to incorrect results and 0 must be included while representing any binary number.
Mistake 3
Confusing binary numbers with decimal numbers
Students may confuse certain binary numbers like 10 (2) with decimal numbers such as 10 (ten). Students have to check where the number is being used before assuming whether the number is a decimal number or a binary number.
Mistake 4
Mixing up odd and even numbers in binary.
Students sometimes tend to make the mistake of writing the last digit of a number. Which would change the whole value of the number. Odd numbers end in 1 and even numbers end in 0.
Mistake 5
Ignoring that binary is a base-2 number system.
When writing binary values, students may forget that binary is a base-2 number system. Which means there are only 2 digits in the binary number system. Writing numbers like 102 and 104 is incorrect.
21 in Binary Examples
Problem 1
Convert 13 to binary
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
Problem 2
Convert 19 to binary using place value method
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
Problem 3
Convert 45 to binary by division by 2 method
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
Problem 4
Convert 58 to binary
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
Problem 5
Convert 100 to binary
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
FAQs on 21 in Binary
1.What is 21 in the binary number system?
2.What is 21 in 8-bit binary?
3.Where is binary used in the real-world?
4.What if we add 1 to 10101 in binary?
5.What is 2 × 10101 (21)
6.How can children in United States use numbers in everyday life to understand 21 in Binary?
7.What are some fun ways kids in United States can practice 21 in Binary with numbers?
8.What role do numbers and 21 in Binary play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve 21 in Binary skills?
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.
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.
