115 LearnersLast updated on August 19th, 2025
98 in Binary
98 in binary is written as 1100010 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 98.
98 in Binary Conversion
The process of converting 98 from decimal to binary involves dividing the number 98 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 98 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 98 by 2 until getting 0 as the quotient is 1100010. Remember, the remainders here have been written upside down.
98 in Binary Chart
In the table shown below, the first column shows the binary digits (1 and 0) as 1100010.
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 1100010 in binary is indeed 98 in the decimal number system.
How to Write 98 in Binary
98 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 98 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 98, 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, 98. 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 98. 98 - 64 = 34.
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, 34. So, the next largest power of 2 is 2⁵, which is 32. Now, we have to write 1 in the 2⁵ place. And then subtract 32 from 34. 34 - 32 = 2.
Step 4 - Identify the next largest power of 2: Now we look for the largest power of 2 that fits into 2. The next largest power of 2 is 2¹, which is equal to 2. Now, we have to write 1 in the 2¹ place. And then subtract 2 from 2. 2 - 2 = 0. We need to stop the process here since the remainder is 0.
Step 5 - Identify the unused place values: In the steps above, we wrote 1 in the 2⁶, 2⁵, and 2¹ places. Now, we can just write 0s in the remaining places, which are 2⁴, 2³, and 2⁰. Now, by substituting the values, we get, 0 in the 2⁰ place 1 in the 2¹ place 0 in the 2² place 0 in the 2³ place 0 in the 2⁴ place 1 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 98 in binary. Therefore, 1100010 is 98 in binary.
Grouping Method: In this method, we divide the number 98 by 2. Let us see the step-by-step conversion.
Step 1 - Divide the given number 98 by 2. 98 / 2 = 49. Here, 49 is the quotient and 0 is the remainder.
Step 2 - Divide the previous quotient (49) by 2. 49 / 2 = 24. Here, the quotient is 24 and the remainder is 1.
Step 3 - Repeat the previous step. 24 / 2 = 12. Now, the quotient is 12, and 0 is the remainder.
Step 4 - Repeat the previous step. 12 / 2 = 6. Here, the quotient is 6 and the remainder is 0.
Step 5 - Repeat the previous step. 6 / 2 = 3. Here, the quotient is 3 and the remainder is 0.
Step 6 - Repeat the previous step. 3 / 2 = 1. Here, the quotient is 1 and the remainder is 1.
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, 98 (decimal) = 1100010 (binary).
Rules for Binary Conversion of 98
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 98. Since the answer is 2⁶, write 1 next to this power of 2. Subtract the value (64) from 98. So, 98 - 64 = 34. Find the largest power of 2 less than or equal to 34. The answer is 2⁵. So, write 1 next to this power. Now, 34 - 32 = 2. Find the largest power of 2 less than or equal to 2. The answer is 2¹. So, write 1 next to this power. Now, 2 - 2 = 0. Since there is no remainder, we can write 0 next to the remaining powers (2⁰, 2², 2³, and 2⁴). Final conversion will be 1100010.
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, 98 is divided by 2 to get 49 as the quotient and 0 as the remainder. Now, 49 is divided by 2. Here, we will get 24 as the quotient and 1 as the remainder. Dividing 24 by 2, we get 12 as the quotient and 0 as the remainder. Continuing this process, we divide 12 by 2 to get 6 as the quotient and 0 as the remainder, and then 6 by 2 to get 3 as the quotient and 0 as the remainder. Next, we divide 3 by 2 to get 1 as the quotient and 1 as the remainder. Finally, 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 98, 1100010.
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 98. 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 98, we use 0s for 2⁰, 2², 2³, and 2⁴, and 1s for 2⁶, 2⁵, and 2¹.
Tips and Tricks for Binary Numbers up to 98
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 98.
Memorize to speed up conversions: We can memorize the binary forms for numbers, especially for smaller numbers.
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… and so on. 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, 98 is even, and its binary form is 1100010. Here, the binary of 98 ends in 0. If the number is odd, then its binary equivalent will end in 1. For example, the binary of 99 (an odd number) is 1100011. 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 in a table will help us remember the conversions.
Common Mistakes and How to Avoid Them in 98 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, 98 can be mistakenly written as 100110 instead of 1100010.
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 98 and 2 instead of dividing 98 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.
98 in Binary Examples
Problem 1
Convert 98 from decimal to binary using the place value method.
1100010
Explanation
2⁶ is the largest power of 2, which is less than or equal to 98.
So place 1 next to 2⁶.
Subtracting 64 from 98, we get 34.
So the next largest power would be 2⁵.
So place another 1 next to 2⁵.
Subtracting 32 from 34, we get 2.
The next largest power is 2¹.
Place another 1 next to 2¹.
Finally, subtracting 2 from 2, we get 0.
Now, we just place 0s in the remaining powers of 2, which are 2⁰, 2², 2³, and 2⁴.
By using this method, we can find the binary form of 98.
Problem 2
Convert 98 from decimal to binary using the division by 2 method.
1100010
Explanation
Divide 98 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 98 to binary using the representation method.
1100010
Explanation
Break the number 98 into powers of 2 and find the largest powers of 2.
We get 2⁶. So 1 is placed next to 2⁶.
Next, 98 - 64 = 34.
The largest power of 2 less than or equal to 34 is 2⁵.
Once again, 1 is placed next to 2⁵.
Now, 34 - 32 = 2, and the largest power of 2 is 2¹.
Place 1 next to 2¹. Subtracting 2 from 2 gives 0.
After getting 0, fill in with zeros for unused powers of 2.
By following this method, we get the binary value of 98 as 1100010.
Problem 4
How is 98 written in decimal, octal, and binary form?
Decimal form - 98 Octal - 142 Binary - 1100010
Explanation
The decimal system is also called the base 10 system.
In this system, 98 is written as 98 only.
We have already seen how 98 is written as 1100010 in binary.
So, let us focus on the octal system, which is base 8.
To convert 98 to octal, we need to divide 98 by 8.
So 98 / 8 = 12 with 2 as the remainder.
In the next step, divide the quotient from the previous step (12) by 8.
So 12 / 8 = 1 with 4 as the remainder.
The division process stops here because the quotient is now 0.
Here, 4 and 2 are the remainders, and they have to be written in reverse order.
So, 142 is the octal equivalent of 98.
Problem 5
Express 98 - 69 in binary.
1111
Explanation
98 - 69 = 29 So, we need to write 29 in binary.
Start by dividing 29 by 2.
We get 14 as the quotient and 1 as the remainder.
Next, divide 14 by 2. Now we get 7 as the quotient and 0 as the remainder.
Divide 7 by 2 to get 3 as the quotient and 1 as the remainder.
Divide 3 by 2 to get 1 as the quotient and 1 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 11101 (binary of 29).
FAQs on 98 in Binary
1.What is 98 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 United States use numbers in everyday life to understand 98 in Binary?
7.What are some fun ways kids in United States can practice 98 in Binary with numbers?
8.What role do numbers and 98 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 98 in Binary skills?
Important Glossaries for 98 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 1100010 (base 2), each digit represents a power of 2.
- Octal: It is the number system with a base of 8. It uses digits from 0 to 7.
- Quotient: The result of division. In binary conversion, it becomes the new dividend in each step.
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.
