110 LearnersLast updated on 20 August 2025
109 in Binary
109 in binary is written as 1101101 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 109 in binary systems.
109 in Binary Conversion
The process of converting 109 from decimal to binary involves dividing the number 109 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 109 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 109 by 2 until getting 0 as the quotient is 1101101. Remember, the remainders here have been written upside down.
109 in Binary Chart
In the table shown below, the first column shows the binary digits (1 and 0) as 1101101.
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 1101101 in binary is indeed 109 in the decimal number system.
How to Write 109 in Binary
109 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 109 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 109, 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, 109. 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 109. 109 - 64 = 45.
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, 45. So, the next largest power of 2 is 2^5, which is 32. Now, we have to write 1 in the 2^5 place. And then subtract 32 from 45. 45 - 32 = 13.
Step 4 - Identify the next largest power of 2: Now find the largest power of 2 that fits into 13. The next largest power is 2^3, which is 8. Write 1 in the 2^3 place and subtract 8 from 13. 13 - 8 = 5.
Step 5 - Identify the next largest power of 2: The largest power of 2 that fits into 5 is 2^2, which is 4. Write 1 in the 2^2 place and subtract 4 from 5. 5 - 4 = 1.
Step 6 - Identify the next largest power of 2: The largest power of 2 that fits into 1 is 2^0, which is 1. Write 1 in the 2^0 place and subtract 1 from 1. 1 - 1 = 0. We need to stop the process here since the remainder is 0.
Step 7 - Identify the unused place values: In the steps above, we wrote 1 in the 2^6, 2^5, 2^3, 2^2, and 2^0 places. Now, we can just write 0s in the remaining places, which are 2^4 and 2^1. Now, by substituting the values, we get: 1 in the 2^0 place 0 in the 2^1 place 1 in the 2^2 place 1 in the 2^3 place 0 in the 2^4 place 1 in the 2^5 place 1 in the 2^6 place
Step 8 - Write the values in reverse order: We now write the numbers upside down to represent 109 in binary. Therefore, 1101101 is 109 in binary.
Grouping Method: In this method, we divide the number 109 by 2. Let us see the step-by-step conversion.
Step 1 - Divide the given number 109 by 2. 109 / 2 = 54. Here, 54 is the quotient and 1 is the remainder.
Step 2 - Divide the previous quotient (54) by 2. 54 / 2 = 27. Here, the quotient is 27 and the remainder is 0.
Step 3 - Repeat the previous step. 27 / 2 = 13. Now, the quotient is 13, and 1 is the remainder.
Step 4 - Repeat the previous step. 13 / 2 = 6. Here, the remainder is 1.
Step 5 - Repeat the previous step. 6 / 2 = 3. Here, the remainder is 0.
Step 6 - Repeat the previous step. 3 / 2 = 1. Here, 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, 109 (decimal) = 1101101 (binary).
Rules for Binary Conversion of 109
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 109. Since the answer is 2^6, write 1 next to this power of 2. Subtract the value (64) from 109. So, 109 - 64 = 45. Find the largest power of 2 less than or equal to 45. The answer is 2^5. So, write 1 next to this power. Subtract 32 from 45. 45 - 32 = 13. Find the largest power of 2 less than or equal to 13. The answer is 2^3. So, write 1 next to this power. Subtract 8 from 13. 13 - 8 = 5. Find the largest power of 2 less than or equal to 5. The answer is 2^2. So, write 1 next to this power. Subtract 4 from 5. 5 - 4 = 1. Find the largest power of 2 less than or equal to 1. The answer is 2^0. So, write 1 next to this power. Now, 1 - 1 = 0. Since there is no remainder, we can write 0 next to the remaining powers (2^4 and 2^1). Final conversion will be 1101101.
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, 109 is divided by 2 to get 54 as the quotient and 1 as the remainder. Now, 54 is divided by 2. Here, we will get 27 as the quotient and 0 as the remainder. Dividing 27 by 2, we get 13 as the quotient and 1 as the remainder. Dividing 13 by 2, we get 6 as the quotient and 1 as the remainder. Dividing 6 by 2, we get 3 as the quotient and 0 as the remainder. Dividing 3 by 2, we get 1 as the quotient and 1 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 109, 1101101.
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 109. 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 109, we use 0s for 2^4 and 2^1 and 1s for 2^6, 2^5, 2^3, 2^2, and 2^0.
Tips and Tricks for Binary Numbers till 109
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 109.
Memorize to speed up conversions: We can memorize the binary forms for numbers 1 to 109.
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 e.g., 108 is even, and its binary form ends in 0. If the number is odd, then its binary equivalent will end in 1. For e.g., the binary of 109 (an odd number) is 1101101. 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 109 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, 109 can be mistakenly written as 1101011 instead of 1101101.
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 109 and 2 instead of dividing 109 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.
109 in Binary Examples
Problem 1
Convert 109 from decimal to binary using the place value method.
1101101
Explanation
2^6 is the largest power of 2, which is less than or equal to 109. So place 1 next to 2^6. Subtracting 64 from 109, we get 45. So the next largest power would be 2^5. So place another 1 next to 2^5. Subtracting 32 from 45 gives 13. The largest power of 2 now is 2^3. So place 1 next to 2^3. Subtracting 8 from 13 gives 5. The next largest power is 2^2. Place 1 next to 2^2 and subtract 4 from 5 to get 1.
Lastly, the largest power is 2^0. Place 1 next to 2^0 and subtract 1 from 1 to get 0. Now, we just place 0s in the remaining powers of 2, which are 2^4 and 2^1. By using this method, we can find the binary form of 109.
Problem 2
Convert 109 from decimal to binary using the division by 2 method.
1101101
Explanation
Divide 109 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 109 to binary using the representation method.
1101101
Explanation
Break the number 109 into powers of 2 and find the largest powers of 2. We get 2^6. So 1 is placed next to 2^6. Next, 109 - 64 = 45. Now, the largest power of 2 is 2^5. Once again, 1 is placed next to 2^5. Now, 45 - 32 = 13. The next largest power is 2^3. 1 is placed next to 2^3. Now, 13 - 8 = 5. The next power of 2 is 2^2. 1 is placed next to 2^2. Now, 5 - 4 = 1. The next power of 2 is 2^0. 1 is placed next to 2^0. Now, 1 - 1 = 0. After getting 0, fill in with zeros for unused powers of 2. By following this method, we get the binary value of 109 as 1101101.
Problem 4
How is 109 written in decimal, octal, and binary form?
Decimal form - 109 Octal - 155 Binary - 1101101
Explanation
The decimal system is also called the base 10 system. In this system, 109 is written as 109 only. We have already seen how 109 is written as 1101101 in binary. So, let us focus on the octal system, which is base 8. To convert 109 to octal, we need to divide 109 by 8. So 109 / 8 = 13 with 5 as the remainder. In the next step, divide the quotient from the previous step (13) by 8. So 13 / 8 = 1 with 5 as the remainder. The division process stops here because the quotient is now 0. Here, 5, 5, and 1 are the remainders, and they have to be written in reverse order. So, 155 is the octal equivalent of 109.
Problem 5
Express 109 - 5 in binary.
110100
Explanation
109 - 5 = 104 So, we need to write 104 in binary. Start by dividing 104 by 2. We get 52 as the quotient and 0 as the remainder. Next, divide 52 by 2. Now we get 26 as the quotient and 0 as the remainder. Divide 26 by 2 to get 13 as the quotient and 0 as the remainder. Divide 13 by 2 to get 6 as the quotient and 1 as the remainder. Divide 6 by 2 to get 3 as the quotient and 0 as the remainder. Divide 3 by 2 to 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. Now write the remainders from bottom to top to get 110100 (binary of 104).
FAQs on 109 in Binary
1.What is 109 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 Kingdom use numbers in everyday life to understand 109 in Binary?
7.What are some fun ways kids in United Kingdom can practice 109 in Binary with numbers?
8.What role do numbers and 109 in Binary play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve 109 in Binary skills?
Important Glossaries for 109 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 as base 2 number system.
- Place value: Every digit has a value based on its position in a given number. For e.g., in 109 (base 10), 1 has occupied the hundreds place, 0 is in the tens place, and 9 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 division in arithmetic, used to determine the next steps in binary conversion.
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.
