104 LearnersLast updated on August 20th, 2025
123 in Binary
123 in binary is written as 1111011 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 123.
123 in Binary Conversion
The process of converting 123 from decimal to binary involves dividing the number 123 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 123 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 123 by 2 until getting 0 as the quotient is 1111011. Remember, the remainders here have been written upside down.
123 in Binary Chart
In the table shown below, the first column shows the binary digits (1 and 0) as 1111011. 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 1111011 in binary is indeed 123 in the decimal number system.
How to Write 123 in Binary
123 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 123 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 123, 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, 123. 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 123. 123 - 64 = 59.
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, 59. So, the next largest power of 2 is 2^5 = 32. Now, we have to write 1 in the 2^5 place. And then subtract 32 from 59. 59 - 32 = 27.
Step 4 - Continue identifying the next powers of 2: Repeat the steps to find the next powers of 2 that fit into the remaining value. For 27, the largest power of 2 is 2^4 = 16. 27 - 16 = 11. For 11, the largest power of 2 is 2^3 = 8. 11 - 8 = 3. For 3, the largest power of 2 is 2^1 = 2. 3 - 2 = 1. Finally, for 1, the largest power of 2 is 2^0 = 1. 1 - 1 = 0.
Step 5 - Write the binary representation: Write a 1 for each of the powers of 2 used and 0 for those that weren’t used. 1 in the 2^6 place 1 in the 2^5 place 1 in the 2^4 place 1 in the 2^3 place 0 in the 2^2 place 1 in the 2^1 place 1 in the 2^0 place Therefore, 1111011 is 123 in binary.
Grouping Method: In this method, we divide the number 123 by 2. Let's see the step-by-step conversion.
Step 1 - Divide the given number 123 by 2. 123 / 2 = 61. Here, 61 is the quotient, and 1 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 process. 30 / 2 = 15. Quotient is 15 and remainder is 0. 15 / 2 = 7. Quotient is 7 and remainder is 1. 7 / 2 = 3. Quotient is 3 and remainder is 1. 3 / 2 = 1. Quotient is 1 and remainder is 1. 1 / 2 = 0. Quotient is 0 and remainder is 1.
Step 4 - Write the remainders from bottom to top. Therefore, 123 (decimal) = 1111011 (binary).
Rules for Binary Conversion of 123
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 123. Since the answer is 2^6, write 1 next to this power of 2. Subtract the value (64) from 123. So, 123 - 64 = 59. Find the largest power of 2 less than or equal to 59. The answer is 2^5. So, write 1 next to this power. Continue this process with 2^4, 2^3, 2^1, and 2^0. Final conversion will be 1111011.
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, 123 is divided by 2 to get 61 as the quotient and 1 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. Repeat the process until the quotient becomes 0. Now, we write the remainders upside down to get the binary equivalent of 123, 1111011.
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: 2^6, 2^5, 2^4, ..., 2^0. Find the largest power that fits into 123. 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 123, we use 1s for 2^6, 2^5, 2^4, 2^3, 2^1, and 2^0 and 0 for 2^2.
Tips and Tricks for Binary Numbers till 123
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 123.
Memorize to speed up conversions: We can memorize the binary forms for numbers 1 to 123. Recognize the patterns: There is a peculiar pattern when converting numbers from decimal to binary. For example: 1 → 1 1 + 1 = 2 → 10 2 + 2 = 4 → 100 4 + 4 = 8 → 1000 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, 4 is even, and its binary form is 100. Here, the binary of 4 ends in 0. If the number is odd, then its binary equivalent will end in 1. For example, the binary of 5 (an odd number) is 101. 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 123 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, 123 can be mistakenly written as 110111 instead of 1111011.
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 123 and 2 instead of dividing 123 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.
123 in Binary Examples
Problem 1
Convert 123 from decimal to binary using the place value method.
1111011
Explanation
2^6 is the largest power of 2, which is less than or equal to 123. So place 1 next to 2^6. Subtracting 64 from 123, we get 59. The next largest power would be 2^5. So place another 1 next to 2^5. Continue the process with powers 2^4, 2^3, 2^1, and 2^0. By using this method, we can find the binary form of 123.
Problem 2
Convert 123 from decimal to binary using the division by 2 method.
1111011
Explanation
Divide 123 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 123 to binary using the representation method.
1111011
Explanation
Break the number 123 into powers of 2 and find the largest powers of 2. We get 2^6. So 1 is placed next to 2^6. Next, 123 - 64 = 59. Now, the largest power of 2 is 2^5. Once again, 1 is placed next to 2^5. Continue the process with the remaining value. By following this method, we get the binary value of 123 as 1111011.
Problem 4
How is 123 written in decimal, octal, and binary form?
Decimal form - 123 Octal - 173 Binary - 1111011
Explanation
The decimal system is also called the base 10 system. In this system, 123 is written as 123. We have already seen how 123 is written as 1111011 in binary. Let us focus on the octal system, which is base 8. To convert 123 to octal, we need to divide 123 by 8. So 123 / 8 = 15 with 3 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. Finally, divide 1 by 8 to get 0 with 1 as the remainder. Writing the remainders in reverse order, we get 173 as the octal equivalent of 123.
Problem 5
Express 123 - 5 in binary.
1111000
Explanation
123 - 5 = 118 So, we need to write 118 in binary. Start by dividing 118 by 2. We get 59 as the quotient and 0 as the remainder. Next, divide 59 by 2. Now we get 29 as the quotient and 1 as the remainder. Continue this process until the quotient is 0. Now, write the remainders from bottom to top to get 1111000 (binary of 118).
FAQs on 123 in Binary
1.What is 123 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 123 in Binary?
7.What are some fun ways kids in United States can practice 123 in Binary with numbers?
8.What role do numbers and 123 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 123 in Binary skills?
Important Glossaries for 123 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 123 (base 10), 1 has occupied the hundreds place, 2 is in the tens place, and 3 is in the ones place.
- Octal: It is the number system with a base of 8. It uses digits from 0 to 7.
- Grouping Method: A method to convert numbers to binary by dividing repeatedly by 2, noting the remainders.
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.
