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113 LearnersLast updated on August 20, 2025
85 in Binary
85 in binary is written as 1010101 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 the binary representation of 85.
85 in Binary Conversion
The process of converting 85 from decimal to binary involves dividing the number 85 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.
For example, the remainders noted down after dividing 85 by 2 until getting 0 as the quotient is 1010101. Remember, the remainders here have been written upside down.
85 in Binary Chart
In the table shown below, the first column shows the binary digits (1 and 0) as 1010101.
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 1010101 in binary is indeed 85 in the decimal number system.
How to Write 85 in Binary
85 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 85 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 85, 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, 85. 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 85. 85 - 64 = 21.
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, 21. So, the next largest power of 2 is 24 = 16, which is less than or equal to 21. Now, we have to write 1 in the 24 place. And then subtract 16 from 21. 21 - 16 = 5.
Step 4 - Repeat the process: We continue by identifying the largest power of 2 that fits into 5, which is 22 = 4. Write 1 in the 22 place and subtract 4 from 5. 5 - 4 = 1.
Step 5 - Write the remaining values: 1 is equal to 20, so write 1 in the 20 place. For all unused places, write 0. Combine the values to get the binary number: 1 in the 26 place 0 in the 25 place 1 in the 24 place 0 in the 23 place 1 in the 22 place 0 in the 21 place 1 in the 20 place Therefore, 1010101 is 85 in binary.
Grouping Method: In this method, we divide the number 85 by 2. Let us see the step-by-step conversion.
Step 1 - Divide the given number 85 by 2. 85 / 2 = 42. Here, 42 is the quotient and 1 is the remainder.
Step 2 - Divide the previous quotient (42) by 2. 42 / 2 = 21. Here, the quotient is 21 and the remainder is 0.
Step 3 - Repeat the previous step. 21 / 2 = 10. Now, the quotient is 10, and 1 is the remainder.
Step 4 - Repeat the previous step. 10 / 2 = 5. The quotient is 5, and the remainder is 0.
Step 5 - Continue the process. 5 / 2 = 2. The quotient is 2, and 1 is the remainder.
Step 6 - Continue the process. 2 / 2 = 1. The quotient is 1, and 0 is the remainder.
Step 7 - Final step. 1 / 2 = 0. 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, 85 (decimal) = 1010101 (binary).
Rules for Binary Conversion of 85
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 85. Since the answer is 26, write 1 next to this power of 2. Subtract the value (64) from 85. So, 85 - 64 = 21. Find the largest power of 2 less than or equal to 21. The answer is 24. So, write 1 next to this power. Repeat the process for the remaining number. Final conversion will be 1010101.
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, 85 is divided by 2 to get 42 as the quotient and 1 as the remainder. Now, 42 is divided by 2. Here, we will get 21 as the quotient and 0 as the remainder. Dividing 21 by 2, we get 10 as the quotient and 1 as the remainder. Continue the process until the quotient becomes 0. Now, we write the remainders upside down to get the binary equivalent of 85, 1010101.
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 85. 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 85, we use 0s for some powers and 1s for others.
Tips and Tricks for Binary Numbers till 85
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 85.
Memorize to speed up conversions: We can memorize the binary forms for numbers 1 to 85.
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 Patterns continue with each power of 2 doubling and adding.
Even and odd rule: Whenever a number is even, its binary form will end in 0. For example, 84 is even, and its binary form ends in 0. If the number is odd, then its binary equivalent will end in 1. For example, the binary of 85 (an odd number) is 1010101.
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 85 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, 85 can be mistakenly written as 1011010 instead of 1010101.
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 85 and 2 instead of dividing 85 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.
85 in Binary Examples
Problem 1
Convert 85 from decimal to binary using the place value method.
1010101
Explanation
26 is the largest power of 2, which is less than or equal to 85.
So place 1 next to 26.
Subtracting 64 from 85, we get 21.
The next largest power would be 24.
So place another 1 next to 24.
Continue the process, and for the remaining powers, place 0s and 1s accordingly to get 1010101.
Problem 2
Convert 85 from decimal to binary using the division by 2 method.
1010101
Explanation
Divide 85 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 85 to binary using the representation method.
1010101
Explanation
Break the number 85 into powers of 2 and find the largest powers of 2.
We get 26. So 1 is placed next to 26.
Next, 85 - 64 = 21.
Now, the largest power of 2 is 24.
Once again, 1 is placed next to 24.
Continue the process for remaining powers.
By following this method, we get the binary value of 85 as 1010101.
Problem 4
How is 85 written in decimal, octal, and binary form?
Decimal form - 85 Octal - 125 Binary - 1010101
Explanation
The decimal system is also called the base 10 system.
In this system, 85 is written as 85 only.
We have already seen how 85 is written as 1010101 in binary.
So, let us focus on the octal system, which is base 8.
To convert 85 to octal, we need to divide 85 by 8.
So 85 / 8 = 10 with 5 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.
The division process stops here because the quotient is now 0.
Here, 5 and 2 are the remainders, and they have to be written in reverse order.
So, 125 is the octal equivalent of 85.
Problem 5
Express 85 - 40 in binary.
101101
Explanation
85 - 40 = 45 So, we need to write 45 in binary.
Start by dividing 45 by 2.
We get 22 as the quotient and 1 as the remainder.
Next, divide 22 by 2.
Now we get 11 as the quotient and 0 as the remainder.
Divide 11 by 2 to get 5 as the quotient and 1 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.
Now write the remainders from bottom to top to get 101101 (binary of 45).
FAQs on 85 in Binary
1.What is 85 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.What are some fun ways kids in Philippines can practice 85 in Binary with numbers?
7.How can children in Philippines use numbers in everyday life to understand 85 in Binary?
8.How can families in Philippines create number-rich environments to improve 85 in Binary skills?
9.What role do numbers and 85 in Binary play in helping children in Philippines develop problem-solving skills?
Important Glossaries for 85 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 a 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 occupies 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.
- Quotient: The result obtained by dividing one number by another.
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.
