118 LearnersLast updated on August 19, 2025
122 in Binary
122 in binary is written as 1111010 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 122.
122 in Binary Conversion
The process of converting 122 from decimal to binary involves dividing the number 122 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 122 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 122 by 2 until getting 0 as the quotient is 1111010. Remember, the remainders here have been written upside down.
122 in Binary Chart
In the table shown below, the first column shows the binary digits (1 and 0) as 1111010. 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 1111010 in binary is indeed 122 in the decimal number system.
How to Write 122 in Binary
122 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 122 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 122, 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, 122. 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 122. 122 - 64 = 58.
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, 58. So, the next largest power of 2 is 2⁵ = 32. Now, we have to write 1 in the 2⁵ place. And then subtract 32 from 58. 58 - 32 = 26.
Step 4 - Identify the next largest power of 2: The next largest power of 2 that fits into 26 is 2⁴ = 16. Write 1 in the 2⁴ place. Then subtract 16 from 26. 26 - 16 = 10.
Step 5 - Identify the next largest power of 2: The next largest power of 2 that fits into 10 is 2³ = 8. Write 1 in the 2³ place. Then subtract 8 from 10. 10 - 8 = 2.
Step 6 - Identify the next largest power of 2: The next largest power of 2 that fits into 2 is 2¹ = 2. Write 1 in the 2¹ place. Then subtract 2 from 2. 2 - 2 = 0. We need to stop the process here since the remainder is 0.
Step 7 - Identify the unused place values: In steps 2, 3, 4, 5, and 6, we wrote 1 in the 2⁶, 2⁵, 2⁴, 2³, and 2¹ places. Now, we can just write 0s in the remaining places, which are 2² and 2⁰. Now, by substituting the values, we get, 0 in the 2⁰ place 1 in the 2¹ place 0 in the 2² place 1 in the 2³ place 1 in the 2⁴ place 1 in the 2⁵ place 1 in the 2⁶ place
Step 8 - Write the values in reverse order: We now write the numbers upside down to represent 122 in binary. Therefore, 1111010 is 122 in binary.
Grouping Method: In this method, we divide the number 122 by 2. Let us see the step-by-step conversion.
Step 1 - Divide the given number 122 by 2. 122 / 2 = 61. Here, 61 is the quotient and 0 is the remainder.
Step 2 - Divide the previous quotient (61) by 2. 61 / 2 = 30. Here, the quotient is 30 and the remainder is 1.
Step 3 - Repeat the previous step. 30 / 2 = 15. Now, the quotient is 15, and 0 is the remainder.
Step 4 - Repeat the previous step. 15 / 2 = 7. Here, the quotient is 7 and the remainder is 1.
Step 5 - Repeat the previous step. 7 / 2 = 3. Here, the quotient is 3 and the remainder is 1.
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, 122 (decimal) = 1111010 (binary).
Rules for Binary Conversion of 122
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 122. Since the answer is 2⁶, write 1 next to this power of 2. Subtract the value (64) from 122. So, 122 - 64 = 58. Find the largest power of 2 less than or equal to 58. The answer is 2⁵. So, write 1 next to this power. Subtract the value (32) from 58. So, 58 - 32 = 26. Find the largest power of 2 less than or equal to 26. The answer is 2⁴. So, write 1 next to this power. Subtract the value (16) from 26. So, 26 - 16 = 10. Find the largest power of 2 less than or equal to 10. The answer is 2³. So, write 1 next to this power. Subtract the value (8) from 10. So, 10 - 8 = 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 (2² and 2⁰). Final conversion will be 1111010.
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, 122 is divided by 2 to get 61 as the quotient and 0 as the remainder. Now, 61 is divided by 2. Here, we will get 30 as the quotient and 1 as the remainder. Dividing 30 by 2, we get 15 as the quotient and 0 as the remainder. Dividing 15 by 2, we get 7 as the quotient and 1 as the remainder. Dividing 7 by 2, we get 3 as the quotient and 1 as the remainder. Dividing 3 by 2, we get 1 as the quotient and 1 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 122, 1111010.
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 122. 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 122, we use 0s for 2² and 2⁰ and 1s for 2⁶, 2⁵, 2⁴, 2³, and 2¹.
Tips and Tricks for Binary Numbers till 122
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 122.
- Memorize to speed up conversions: We can memorize the binary forms for numbers 1 to 122.
- 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 + 64 = 128 → 10000000…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, 122 is even, and its binary form is 1111010. Here, the binary of 122 ends in 0. If the number is odd, then its binary equivalent will end in 1. For example, the binary of 123 (an odd number) is 1111011. 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 122 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, 122 can be mistakenly written as 1011101 instead of 1111010.
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 122 and 2 instead of dividing 122 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.
122 in Binary Examples
Problem 1
Convert 122 from decimal to binary using the place value method.
1111010
Explanation
2⁶ is the largest power of 2, which is less than or equal to 122.
So place 1 next to 2⁶.
Subtracting 64 from 122, we get 58.
So the next largest power would be 2⁵.
So place another 1 next to 2⁵.
Now, subtracting 32 from 58, we get 26.
The next largest power is 2⁴.
Place 1 next to 2⁴.
Subtract 16 from 26, resulting in 10.
The next largest power is 2³.
Place 1 next to 2³.
Subtract 8 from 10, resulting in 2.
The next largest power is 2¹.
Place 1 next to 2¹.
Subtract 2 from 2, resulting in 0.
Now, we just place 0s in the remaining powers of 2, which are 2² and 2⁰.
By using this method, we can find the binary form of 122.
Problem 2
Convert 122 from decimal to binary using the division by 2 method.
1111010
Explanation
Divide 122 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 122 to binary using the representation method.
1111010
Explanation
Break the number 122 into powers of 2 and find the largest powers of 2.
We get 2⁶. So 1 is placed next to 2⁶. Next, 122 - 64 = 58.
The largest power of 2 is 2⁵.
Place 1 next to 2⁵. Next, 58 - 32 = 26.
The largest power of 2 is 2⁴. Place 1 next to 2⁴
. Next, 26 - 16 = 10.
The largest power of 2 is 2³.
Place 1 next to 2³. Next, 10 - 8 = 2.
The largest power of 2 is 2¹.
Place 1 next to 2¹.
Now, 2 - 2 = 0.
After getting 0, fill in with zeros for unused powers of 2.
By following this method, we get the binary value of 122 as 1111010.
Problem 4
How is 122 written in decimal, octal, and binary form?
Decimal form - 122 Octal - 172 Binary - 1111010
Explanation
The decimal system is also called the base 10 system.
In this system, 122 is written as 122 only.
We have already seen how 122 is written as 1111010 in binary.
So, let us focus on the octal system, which is base 8.
To convert 122 to octal, we need to divide 122 by 8. 122 / 8 = 15 with 2 as the remainder.
In the next step, divide the quotient from the previous step (15) by 8.
So 15 / 8 = 1 with 7 as the remainder.
The division process stops here because the quotient is now 0.
Here, 7 and 2 are the remainders, and they have to be written in reverse order.
So, 172 is the octal equivalent of 122.
Problem 5
Express 122 - 5 in binary.
111011
Explanation
122 - 5 = 117
So, we need to write 117 in binary.
Start by dividing 117 by 2.
We get 58 as the quotient and 1 as the remainder.
Next, divide 58 by 2.
Now we get 29 as the quotient and 0 as the remainder.
Divide 29 by 2. Now we get 14 as the quotient and 1 as the remainder.
Divide 14 by 2.
Now we get 7 as the quotient and 0 as the remainder.
Divide 7 by 2.
Now we get 3 as the quotient and 1 as the remainder.
Divide 3 by 2.
Now we get 1 as the quotient and 1 as the remainder.
Divide 1 by 2.
Now we get 0 as the quotient and 1 as the remainder.
Now write the remainders from bottom to top to get 111011 (binary of 117).
FAQs on 122 in Binary
1.What is 122 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 122 in Binary?
7.What are some fun ways kids in United States can practice 122 in Binary with numbers?
8.What role do numbers and 122 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 122 in Binary skills?
Important Glossaries for 122 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 122 (base 10), 1 has occupied the hundreds place, 2 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 of a division process, representing how many times the divisor fits into the dividend.
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.
