Summarize this article:
114 LearnersLast updated on 17 August 2025
155 in Binary
155 in binary is written as 10011011 because the binary system uses only two digits, 0 and 1, to represent numbers. This number system is widely used in computer systems. In this topic, we are going to learn about the binary representation of 155.
155 in Binary Conversion
The process of converting 155 from decimal to binary involves dividing the number 155 by 2. It is 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 155 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 155 by 2 until getting 0 as the quotient is 10011011. Remember, the remainders here have been written upside down.
155 in Binary Chart
In the table shown below, the first column shows the binary digits (1 and 0) as 10011011.
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 10011011 in binary is indeed 155 in the decimal number system.
How to Write 155 in Binary
155 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 155 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
28 = 256 Since 256 is greater than 155, we stop at 27 = 128.
Step 2 - Identify the largest power of 2: In the previous step, we stopped at 27 = 128. 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, 155. Since 2^7 is the number we are looking for, write 1 in the 27 place. Now the value of 27, which is 128, is subtracted from 155. 155 - 128 = 27.
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, 27. So, the next largest power of 2 is 24, which is less than or equal to 27. Now, we have to write 1 in the 24 place. And then subtract 16 from 27. 27 - 16 = 11.
Step 4 - Identify the next largest power of 2: Continuing from the previous result, the next largest power of 2 that fits into 11 is 23. Write 1 in the 23 place. Subtract 8 from 11. 11 - 8 = 3.
Step 5 - Identify the next largest power of 2: The next largest power of 2 that fits into 3 is 21. Write 1 in the 21 place. Subtract 2 from 3. 3 - 2 = 1.
Step 6 - Identify the next largest power of 2: The last remaining number is 1, which fits into 20. Write 1 in the 20 place. 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 steps 2, 3, 4, 5, and 6, we wrote 1 in the 27, 24, 23, 21, and 20 places. Now, we can just write 0s in the remaining places, which are 26, 25, and 22. Now, by substituting the values, we get: 0 in the 26 place 0 in the 25 place 1 in the 24 place 1 in the 23 place 0 in the 22 place 1 in the 21 place 1 in the 20 place
Step 8 - Write the values in reverse order: We now write the numbers upside down to represent 155 in binary. Therefore, 10011011 is 155 in binary.
Grouping Method: In this method, we divide the number 155 by 2. Let us see the step-by-step conversion.
Step 1 - Divide the given number 155 by 2. 155 / 2 = 77. Here, 77 is the quotient and 1 is the remainder.
Step 2 - Divide the previous quotient (77) by 2. 77 / 2 = 38. Here, the quotient is 38 and the remainder is 1.
Step 3 - Repeat the previous step. 38 / 2 = 19. Now, the quotient is 19, and 0 is the remainder.
Step 4 - Repeat the previous step. 19 / 2 = 9. Here, the quotient is 9, and the remainder is 1.
Step 5 - Repeat the previous step. 9 / 2 = 4. Here, the quotient is 4, and the remainder is 1.
Step 6 - Repeat the previous step. 4 / 2 = 2. Here, the quotient is 2, and the remainder is 0.
Step 7 - Repeat the previous step. 2 / 2 = 1. Here, the quotient is 1, and the remainder is 0.
Step 8 - Repeat the previous step. 1 / 2 = 0. Here, the remainder is 1. And we stop the division here because the quotient is 0.
Step 9 - Write down the remainders from bottom to top. Therefore, 155 (decimal) = 10011011 (binary).
Rules for Binary Conversion of 155
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 155. Since the answer is 27, write 1 next to this power of 2. Subtract the value (128) from 155. So, 155 - 128 = 27. Find the largest power of 2 less than or equal to 27. The answer is 24. So, write 1 next to this power. Now, 27 - 16 = 11. Continue this process until you reach 0. Add 0s for unused powers. Final conversion will be 10011011.
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, 155 is divided by 2 to get 77 as the quotient and 1 as the remainder. Now, 77 is divided by 2. Here, we will get 38 as the quotient and 1 as the remainder. Dividing 38 by 2, we get 19 as the quotient and 0 as the remainder. Divide 19 by 2 to get 9 as the quotient and 1 as the remainder. Divide 9 by 2 to get 4 as the quotient and 1 as the remainder. Divide 4 by 2 to get 2 as the quotient and 0 as the remainder. Divide 2 by 2 to get 1 as the quotient and 0 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 155, 10011011.
Rule 3: Representation Method
This rule also involves breaking the number into powers of 2. Identify the powers of 2 and write it down in decreasing order, i.e., 27, 26, 25, 24, 23, 22, 21, and 20. Find the largest power that fits into 155. 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 155, we use 0s for 26, 25, and 22 and 1s for 27, 24, 23, 21, and 20.
Tips and Tricks for Binary Numbers till 155
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 155.
Memorize to speed up conversions: We can memorize the binary forms for numbers in small ranges to speed up conversions.
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, 154 is even and its binary form is 10011010. Here, the binary of 154 ends in 0. If the number is odd, then its binary equivalent will end in 1. For example, the binary of 155 (an odd number) is 10011011. 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 155 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, 155 can be mistakenly written as 11001101 instead of 10011011.
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 155 and 2 instead of dividing 155 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.
155 in Binary Examples
Problem 1
Convert 155 from decimal to binary using the place value method.
10011011
Explanation
27 is the largest power of 2, which is less than or equal to 155.
So place 1 next to 27.
Subtracting 128 from 155, we get 27.
So the next largest power would be 24.
So place another 1 next to 24.
Now, subtracting 16 from 27, we get 11.
Continue this process until you reach 0.
By using this method, we can find the binary form of 155.
Problem 2
Convert 155 from decimal to binary using the division by 2 method.
10011011
Explanation
Divide 155 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 155 to binary using the representation method.
10011011
Explanation
Break the number 155 into powers of 2 and find the largest powers of 2.
We get 27. So 1 is placed next to 27.
Next, 155 - 128 = 27.
Now, the largest power of 2 is 24.
Once again, 1 is placed next to 24.
Continue this process 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 155 as 10011011.
Problem 4
How is 155 written in decimal, octal, and binary form?
Decimal form - 155 Octal - 233 Binary - 10011011
Explanation
The decimal system is also called the base 10 system.
In this system, 155 is written as 155 only.
We have already seen how 155 is written as 10011011 in binary.
So, let us focus on the octal system, which is base 8.
To convert 155 to octal, we need to divide 155 by 8.
So 155 / 8 = 19 with 3 as the remainder.
In the next step, divide the quotient from the previous step (19) by 8.
So 19 / 8 = 2 with 3 as the remainder.
The division process stops here because the quotient is now 0.
Here, 3 and 3 are the remainders, and they have to be written in reverse order.
So, 233 is the octal equivalent of 155.
Problem 5
Express 155 - 10 in binary.
10010011
Explanation
155 - 10 = 145
So, we need to write 145 in binary.
Start by dividing 145 by 2.
We get 72 as the quotient and 1 as the remainder.
Next, divide 72 by 2. Now we get 36 as the quotient and 0 as the remainder.
Divide 36 by 2 to get 18 as the quotient and 0 as the remainder.
Divide 18 by 2 to get 9 as the quotient and 0 as the remainder.
Divide 9 by 2 to get 4 as the quotient and 1 as the remainder.
Divide 4 by 2 to get 2 as the quotient and 0 as the remainder.
Divide 2 by 2 to get 1 as the quotient and 0 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 10010011 (binary of 145).
FAQs on 155 in Binary
1.What is 155 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 families in Australia create number-rich environments to improve 155 in Binary skills?
7.What are some fun ways kids in Australia can practice 155 in Binary with numbers?
8.How can children in Australia use numbers in everyday life to understand 155 in Binary?
9.What role do numbers and 155 in Binary play in helping children in Australia develop problem-solving skills?
Important Glossaries for 155 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 100 (base 10), 1 occupies the hundreds place, 0 is in the tens place, and another 0 is in the ones place.
- Octal: It is the number system with a base of 8. It uses digits from 0 to 7.
- Quotient and Remainder: The result of a division operation, where the quotient is the number of times the divisor can be divided into the dividend, and the remainder is the leftover part.
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.
