106 LearnersLast updated on August 20, 2025
87 in Binary
87 in binary is written as 1010111 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 87.
87 in Binary Conversion
The process of converting 87 from decimal to binary involves dividing the number 87 by 2. It is divided by 2 because the binary number system uses only two 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 87 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 87 by 2 until getting 0 as the quotient are 1010111. Remember, the remainders here have been written upside down.
87 in Binary Chart
In the table shown below, the first column shows the binary digits (1 and 0) as 87. 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 1010111 in binary is indeed 87 in the decimal number system.
How to Write 87 in Binary
87 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 87 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. 2^0 = 1 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 Since 128 is greater than 87, we stop at 2^6 = 64.
Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2^6 = 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, 87. Since 2^6 is the number we are looking for, write 1 in the 2^6 place. Now the value of 2^6, which is 64, is subtracted from 87. 87 - 64 = 23.
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, 23. So, the next largest power of 2 is 2^4, which is 16. Now, we have to write 1 in the 2^4 places. And then subtract 16 from 23. 23 - 16 = 7.
Step 4 - Repeat the process for the remainder: Now, find the largest power of 2 that fits into 7, which is 2^2 = 4. Write 1 in the 2^2 place and subtract 4 from 7. 7 - 4 = 3. Then, use 2^1 = 2 for the remaining 3, write 1 in the 2^1 place and subtract 2 from 3. 3 - 2 = 1. Finally, use 2^0 = 1 for the last remaining 1, write 1 in the 2^0 place and subtract 1 from 1. 1 - 1 = 0.
Step 5 - Identify the unused place values: In step 2, step 3, and step 4, we wrote 1 in the 2^6, 2^4, 2^2, 2^1, and 2^0 places. Now, we can just write 0s in the remaining places, which are 2^5 and 2^3. Now, by substituting the values, we get: 1 in the 2^0 place 1 in the 2^1 place 1 in the 2^2 place 0 in the 2^3 place 1 in the 2^4 place 0 in the 2^5 place 1 in the 2^6 place
Step 6 - Write the values in reverse order: We now write the numbers upside down to represent 87 in binary. Therefore, 1010111 is 87 in binary.
Grouping Method: In this method, we divide the number 87 by 2. Let us see the step-by-step conversion.
Step 1 - Divide the given number 87 by 2. 87 / 2 = 43. Here, 43 is the quotient and 1 is the remainder.
Step 2 - Divide the previous quotient (43) by 2. 43 / 2 = 21. Here, the quotient is 21 and the remainder is 1.
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 0 is the remainder.
Step 5 - Continue dividing until reaching a quotient of 0. 5 / 2 = 2. The quotient is 2, and 1 is the remainder. 2 / 2 = 1. The quotient is 1, and 0 is the remainder. 1 / 2 = 0. The quotient is 0, and 1 is the remainder.
Step 6 - Write down the remainders from bottom to top. Therefore, 87 (decimal) = 1010111 (binary).
Rules for Binary Conversion of 87
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 87. Since the answer is 2^6, write 1 next to this power of 2. Subtract the value (64) from 87. So, 87 - 64 = 23. Find the largest power of 2 less than or equal to 23. The answer is 2^4. So, write 1 next to this power. Now, 23 - 16 = 7. Continue the process, writing 1 or 0 based on the remaining numbers. Final conversion will be 1010111.
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, 87 is divided by 2 to get 43 as the quotient and 1 as the remainder. Now, 43 is divided by 2. Here, we will get 21 as the quotient and 1 as the remainder. Dividing 21 by 2, we get 10 as the quotient and 1 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 1 as the remainder and 0 as the quotient. We stop the division once the quotient becomes 0. Now, we write the remainders upside down to get the binary equivalent of 87, 1010111.
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., 2^6, 2^5, 2^4, 2^3, 2^2, 2^1, and 2^0. Find the largest power that fits into 87. 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 87, we use 0s for 2^5 and 2^3 and 1s for 2^6, 2^4, 2^2, 2^1, and 2^0.
Tips and Tricks for Binary Numbers till 87
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 87.
Memorize to speed up conversions: We can memorize the binary forms for numbers 1 to 87. 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 Continue doubling and adding. This is also called the double and add rule.
Even and odd rule: Whenever a number is even, its binary form will end in 0. For example, 88 is even, and its binary form is 1011000. If the number is odd, then its binary equivalent will end in 1. For example, the binary of 87 (an odd number) is 1010111. 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 87 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, 87 can be mistakenly written as 110101 instead of 1010111.
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 87 and 2 instead of dividing 87 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.
87 in Binary Examples
Problem 1
Convert 87 from decimal to binary using the place value method.
1010111
Explanation
2^6 is the largest power of 2, which is less than or equal to 87. So place 1 next to 2^6. Subtracting 64 from 87, we get 23. So the next largest power would be 2^4. So place another 1 next to 2^4. Now, subtracting 16 from 23, we get 7. Continue with 2^2 and 2^1, placing 1s accordingly until you reach 0. By using this method, we can find the binary form of 87.
Problem 2
Convert 87 from decimal to binary using the division by 2 method.
1010111
Explanation
Divide 87 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 87 to binary using the representation method.
1010111
Explanation
Break the number 87 into powers of 2 and find the largest powers of 2. We get 2^6. So 1 is placed next to 2^6. Next, 87 - 64 = 23. Now, the largest power of 2 is 2^4. Once again, 1 is placed next to 2^4. Continue with 2^2, 2^1, and 2^0, placing 1s until you reach 0. After getting 0, fill in with zeros for unused powers of 2. By following this method, we get the binary value of 87 as 1010111.
Problem 4
How is 87 written in decimal, octal, and binary form?
Decimal form - 87 Octal - 127 Binary - 1010111
Explanation
The decimal system is also called the base-10 system. In this system, 87 is written as 87. We have already seen how 87 is written as 1010111 in binary. So, let us focus on the octal system, which is base-8. To convert 87 to octal, we need to divide 87 by 8. So 87 / 8 = 10 with 7 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, 2, 7, and 1 are the remainders, and they have to be written in reverse order. So, 127 is the octal equivalent of 87.
Problem 5
Express 87 - 5 in binary.
1010000
Explanation
87 - 5 = 82 So, we need to write 82 in binary. Start by dividing 82 by 2. We get 41 as the quotient and 0 as the remainder. Next, divide 41 by 2. Now we get 20 as the quotient and 1 as the remainder. Continue dividing until the quotient is 0. Now write the remainders from bottom to top to get 1010000 (binary of 82).
FAQs on 87 in Binary
1.What is 87 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 87 in Binary?
7.What are some fun ways kids in Philippines can practice 87 in Binary with numbers?
8.What role do numbers and 87 in Binary play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve 87 in Binary skills?
Important Glossaries for 87 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 1010111 (base 2), the digits have varying place values.
- 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.
