Summarize this article:
149 LearnersLast updated on August 19, 2025
81 in Binary
81 in binary is written as 1010001 because the binary system uses only two digits, 0 and 1, to represent numbers. This number system is used widely in computer systems. In this topic, we are going to learn about converting the number 81 to its binary equivalent.
81 in Binary Conversion
The process of converting 81 from decimal to binary involves dividing the number 81 by 2. Here, it is getting divided by 2 because the binary number system uses only 2 digits (0 and 1). The quotient becomes the dividend in the next step, and the process continues until the quotient becomes 0.
This is a commonly used method to convert 81 to binary. In the last step, the remainder is noted down bottom side up, and that becomes the converted value. For example, the remainders noted down after dividing 81 by 2 until getting 0 as the quotient is 1010001. Remember, the remainders here have been written upside down.
81 in Binary Chart
In the table shown below, the first column shows the binary digits (1 and 0) as 1010001. The second column represents the place values of each digit, and the third column is the value calculation, where the binary digits are multiplied by their corresponding place values.
The results of the third column can be added to cross-check if 1010001 in binary is indeed 81 in the decimal number system.
How to Write 81 in Binary
81 can be converted easily from decimal to binary. The methods mentioned below will help us convert the number. Let’s see how it is done.
Expansion Method: Let us see the step-by-step process of converting 81 using the expansion method.
Step 1 - Figure out the place values: In the binary system, each place value is a power of 2. Therefore, in the first step, we will ascertain the powers of 2.
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
Since 128 is greater than 81, we stop at 26 = 64.
Step 2 - Identify the largest power of 2: In the previous step, we stopped at 26 = 64. This is because in this step, we have to identify the largest power of 2, which is less than or equal to the given number, 81. Since 26 is the number we are looking for, write 1 in the 26 place. Now the value of 26, which is 64, is subtracted from 81. 81 - 64 = 17.
Step 3 - Identify the next largest power of 2: In this step, we need to find the largest power of 2 that fits into the result of the previous step, 17. So, the next largest power of 2 is 24, which is less than or equal to 17. Now, we have to write 1 in the 24 place. And then subtract 16 from 17. 17 - 16 = 1.
Step 4 - Identify the next largest power of 2: Now, we focus on 1. The largest power of 2 that fits into 1 is 20. Write 1 in the 20 place.
Step 5 - Identify the unused place values: In step 2, step 3, and step 4, we wrote 1 in the 26, 24, and 20 places. Now, we can just write 0s in the remaining places, which are 25, 23, 22, and 21. Now, by substituting the values, we get, 1 in the 20 place 0 in the 21 place 0 in the 22 place 0 in the 23 place 1 in the 24 place 0 in the 25 place 1 in the 26 place
Step 6 - Write the values in reverse order: We now write the numbers upside down to represent 81 in binary. Therefore, 1010001 is 81 in binary.
Grouping Method: In this method, we divide the number 81 by 2. Let us see the step-by-step conversion.
Step 1 - Divide the given number 81 by 2. 81 / 2 = 40. Here, 40 is the quotient and 1 is the remainder.
Step 2 - Divide the previous quotient (40) by 2. 40 / 2 = 20. Here, the quotient is 20 and the remainder is 0.
Step 3 - Repeat the previous step. 20 / 2 = 10. Now, the quotient is 10 and 0 is the remainder.
Step 4 - Repeat the previous step. 10 / 2 = 5. Here, the remainder is 0.
Step 5 - Repeat the previous step. 5 / 2 = 2. Here, the quotient is 2 and the remainder is 1.
Step 6 - Repeat the previous step. 2 / 2 = 1. Here, the remainder is 0.
Step 7 - Repeat the previous step. 1 / 2 = 0. Here, the remainder is 1. And we stop the division here because the quotient is 0.
Step 8 - Write down the remainders from bottom to top. Therefore, 81 (decimal) = 1010001 (binary).
Rules for Binary Conversion of 81
There are certain rules to follow when converting any number to binary. Some of them are mentioned below:
Rule 1: Place Value Method
This is one of the most commonly used rules to convert any number to binary. The place value method is the same as the expansion method, where we need to find the largest power of 2. Let’s see a brief step-by-step explanation to understand the first rule. Find the largest power of 2 less than or equal to 81. Since the answer is 26, write 1 next to this power of 2. Subtract the value (64) from 81. So, 81 - 64 = 17. Find the largest power of 2 less than or equal to 17. The answer is 24. So, write 1 next to this power. Now, 17 - 16 = 1. Find the largest power of 2 less than or equal to 1. The answer is 20. So, write 1 next to this power. Since there is no remainder, we can write 0 next to the remaining powers (25, 23, 22, and 21). Final conversion will be 1010001.
Rule 2: Division by 2 Method
The division by 2 method is the same as the grouping method. A brief step-by-step explanation is given below for better understanding. First, 81 is divided by 2 to get 40 as the quotient and 1 as the remainder. Now, 40 is divided by 2. Here, we will get 20 as the quotient and 0 as the remainder. Dividing 20 by 2, we get 10 as the quotient and 0 as the remainder. Divide 10 by 2 to get 5 as the quotient and 0 as the remainder. Divide 5 by 2 to get 2 as the quotient and 1 as the remainder. Divide 2 by 2 to get 1 as the quotient and 0 as the remainder. Divide 1 by 2 to get 0 as the quotient and 1 as the remainder. We stop the division once the quotient becomes 0. Now, we write the remainders upside down to get the binary equivalent of 81, 1010001.
Rule 3: Representation Method
This rule also involves breaking the number into powers of 2. Identify the powers of 2 and write them down in decreasing order, i.e., 26, 25, 24, 23, 22, 21, and 20. Find the largest power that fits into 81. Repeat the process and allocate 1s and 0s to the suitable powers of 2. Combine the digits (0 and 1) to get the binary result.
Rule 4: Limitation Rule
The limitation of the binary system is that only 0s and 1s can be used to represent numbers. The system doesn’t use any other digits other than 0 and 1. This is a base 2 number system, where the binary places represent powers of 2. So, every digit is either a 0 or a 1. To convert 81, we use 0s for 25, 23, 22, and 21, and 1s for 26, 24, and 20.
Tips and Tricks for Binary Numbers till 81
Learning a few tips and tricks is a great way to solve any mathematical problems easily. Let us take a look at some tips and tricks for binary numbers up to 81.
- Memorize to speed up conversions: We can memorize the binary forms for numbers 1 to 81.
- Recognize the patterns: There is a peculiar pattern when converting numbers from decimal to binary. 1 → 1 1 + 1 = 2 → 10 2 + 2 = 4 → 100 4 + 4 = 8 → 1000 8 + 8 = 16 → 10000 16 + 16 = 32 → 100000 32 + 32 = 64 → 1000000 64 + 17 = 81 → 1010001
- Even and odd rule: Whenever a number is even, its binary form will end in 0. For example, 10 is even and its binary form is 1010. Here, the binary of 10 ends in 0. If the number is odd, then its binary equivalent will end in 1. For example, the binary of 81 (an odd number) is 1010001. As you can see, the last digit here is 1.
- Cross-verify the answers: Once the conversion is done, we can cross-verify the answers by converting the number back to the decimal form. This will eliminate any unforeseen errors in conversion.
- Practice by using tables: Writing the decimal numbers and their binary equivalents on a table will help us remember the conversions.
Common Mistakes and How to Avoid Them in 81 in Binary
Here, let us take a look at some of the most commonly made mistakes while converting numbers to binary.
Mistake 1
Writing the Remainders From Top to Bottom
Always remember to read and write the remainders from bottom to top.
After converting a number to binary using any of the methods mentioned above, it is important to read the remainders upside down to get the correct value.
Mistake 2
Misplacing 1s and 0s
Since the binary system uses only 1s and 0s, we have to be careful while representing any number in its binary form.
For example, 81 can be mistakenly written as 1010010 instead of 1010001.
Mistake 3
Not Practicing Enough
Converting numbers from decimal to binary on a regular basis will help boost our confidence and minimize mistakes.
Practice daily to become an expert in converting numbers to binary.
Mistake 4
Adding Instead of Dividing
When using the grouping method, students may incorrectly add 81 and 2 instead of dividing 81 by 2.
Always remember that division is used in the process to convert numbers to binary.
Mistake 5
Stopping the Division Too Early
It is important to continue the division process until the quotient becomes 0.
Failing to do so will result in errors in the final calculation.
81 in Binary Examples
Problem 1
Convert 81 from decimal to binary using the place value method.
1010001
Explanation
26 is the largest power of 2, which is less than or equal to 81.
So place 1 next to 26.
Subtracting 64 from 81, we get 17.
So the next largest power would be 24.
So place another 1 next to 24.
Now, subtracting 16 from 17, we get 1.
The largest power of 2 now is 20.
So place another 1 next to 20.
Now, we just place 0s in the remaining powers of 2, which are 25, 23, 22, and 21.
By using this method, we can find the binary form of 81.
Problem 2
Convert 81 from decimal to binary using the division by 2 method.
1010001
Explanation
Divide 81 by 2. In the next step, the quotient becomes the new dividend.
Continue the process until the quotient becomes 0.
Now, write the remainders upside down to get the final result.
Problem 3
Convert 81 to binary using the representation method.
1010001
Explanation
Break the number 81 into powers of 2 and find the largest powers of 2.
We get 26. So 1 is placed next to 26.
Next, 81 - 64 = 17.
Now, the largest power of 2 is 24.
Once again, 1 is placed next to 24.
Next, 17 - 16 = 1.
Now, the largest power of 2 is 20.
Once again, 1 is placed next to 20.
After getting 0, fill in with zeros for unused powers of 2.
By following this method, we get the binary value of 81 as 1010001.
Problem 4
How is 81 written in decimal, octal, and binary form?
Decimal form - 81 Octal - 121 Binary - 1010001
Explanation
The decimal system is also called the base 10 system.
In this system, 81 is written as 81 only.
We have already seen how 81 is written as 1010001 in binary.
So, let us focus on the octal system, which is base 8.
To convert 81 to octal, we need to divide 81 by 8.
So 81 / 8 = 10 with 1 as the remainder. In the next step, divide the quotient from the previous step (10) by 8.
So 10 / 8 = 1 with 2 as the remainder.
Now, divide 1 by 8 to get 0 with 1 as the remainder.
The division process stops here because the quotient is now 0.
Here, 1, 2, and 1 are the remainders, and they have to be written in reverse order.
So, 121 is the octal equivalent of 81.
Problem 5
Express 81 - 1 in binary.
1010000
Explanation
81 - 1 = 80
So, we need to write 80 in binary.
Start by dividing 80 by 2.
We get 40 as the quotient and 0 as the remainder.
Next, divide 40 by 2.
Now we get 20 as the quotient and 0 as the remainder.
Next, divide 20 by 2.
Now we get 10 as the quotient and 0 as the remainder.
Next, divide 10 by 2.
Now we get 5 as the quotient and 0 as the remainder.
Next, divide 5 by 2.
Now we get 2 as the quotient and 1 as the remainder.
Next, divide 2 by 2.
Now we get 1 as the quotient and 0 as the remainder.
Finally, divide 1 by 2 to get 0 as the quotient and 1 as the remainder.
Now write the remainders from bottom to top to get 1010000 (binary of 80).
FAQs on 81 in Binary
1.What is 81 in binary?
2.Where is binary used in the real world?
3.What is the difference between binary and decimal numbers?
4.Can we do mental conversion of decimal to binary?
5.How to practice conversion regularly?
6.How can children in Philippines use numbers in everyday life to understand 81 in Binary?
7.What are some fun ways kids in Philippines can practice 81 in Binary with numbers?
8.What role do numbers and 81 in Binary play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve 81 in Binary skills?
Important Glossaries for 81 in Binary
- Decimal: It is the base 10 number system which uses digits from 0 to 9.
- Binary: This number system uses only 0 and 1. It is also called the base 2 number system.
- Place value: Every digit has a value based on its position in a given number. For example, in 102 (base 10), 1 has occupied the hundreds place, 0 is in the tens place, and 2 is in the ones place.
- Octal: It is the number system with a base of 8. It uses digits from 0 to 7.
- Power of 2: Refers to numbers that are the result of raising 2 to an exponent, used in the binary numbering system.
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.
