103 LearnersLast updated on August 19th, 2025
156 in Binary
156 in binary is written as 10011100 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 converting 156 to binary.
156 in Binary Conversion
The process of converting 156 from decimal to binary involves dividing the number 156 by 2. Here, 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 156 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 156 by 2 until getting 0 as the quotient is 10011100. Remember, the remainders here have been written upside down.
156 in Binary Chart
In the table shown below, the first column shows the binary digits (1 and 0) as 10011100. 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 10011100 in binary is indeed 156 in the decimal number system.
How to Write 156 in Binary
156 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 156 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 less than 156, we stop at 2^7 = 128.
Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2^7 = 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, 156. Since 2^7 is the number we are looking for, write 1 in the 2^7 place. Now the value of 2^7, which is 128, is subtracted from 156. 156 - 128 = 28.
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, 28. So, the next largest power of 2 is 2^4, which is less than or equal to 28. Now, we have to write 1 in the 2^4 place. And then subtract 16 from 28. 28 - 16 = 12.
Step 4 - Continue the process: The next largest power of 2 that fits into 12 is 2^3, so write 1 in the 2^3 place and subtract 8 from 12. 12 - 8 = 4. Finally, the largest power of 2 that fits into 4 is 2^2, so write 1 in the 2^2 place and subtract 4 from 4. 4 - 4 = 0. We need to stop the process here since the remainder is 0.
Step 5 - Identify the unused place values: In step 2, step 3, and step 4, we wrote 1 in the 2^7, 2^4, 2^3, and 2^2 places. Now, we can just write 0s in the remaining places, which are 2^6, 2^5, 2^1, and 2^0. Now, by substituting the values, we get, 0 in the 2^0 place 0 in the 2^1 place 1 in the 2^2 place 1 in the 2^3 place 1 in the 2^4 place 0 in the 2^5 place 0 in the 2^6 place 1 in the 2^7 place
Step 6 - Write the values in reverse order: We now write the numbers upside down to represent 156 in binary. Therefore, 10011100 is 156 in binary.
Grouping Method: In this method, we divide the number 156 by 2. Let us see the step-by-step conversion.
Step 1 - Divide the given number 156 by 2. 156 / 2 = 78. Here, 78 is the quotient and 0 is the remainder.
Step 2 - Divide the previous quotient (78) by 2. 78 / 2 = 39. Here, the quotient is 39 and the remainder is 0.
Step 3 - Repeat the previous step. 39 / 2 = 19. Now, the quotient is 19, and 1 is the remainder.
Step 4 - Repeat the previous step. 19 / 2 = 9. Here, the quotient is 9, and 1 is the remainder.
Step 5 - Continue dividing. 9 / 2 = 4. The quotient is 4, and the remainder is 1. Step 6 - Continue dividing. 4 / 2 = 2. The quotient is 2, and the remainder is 0.
Step 7 - Continue dividing. 2 / 2 = 1. The quotient is 1, and the remainder is 0.
Step 8 - Continue dividing. 1 / 2 = 0. Here, the quotient is 0, and the remainder is 1. We stop the division here because the quotient is 0.
Step 9 - Write down the remainders from bottom to top. Therefore, 156 (decimal) = 10011100 (binary).
Rules for Binary Conversion of 156
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 156. Since the answer is 2^7, write 1 next to this power of 2. Subtract the value (128) from 156. So, 156 - 128 = 28. Find the largest power of 2 less than or equal to 28. The answer is 2^4. So, write 1 next to this power. Now, 28 - 16 = 12. Continue the process until the remainder is 0. Final conversion will be 10011100.
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, 156 is divided by 2 to get 78 as the quotient and 0 as the remainder. Now, 78 is divided by 2. Here, we will get 39 as the quotient and 0 as the remainder. Dividing 39 by 2, we get 19 as the quotient and 1 as the remainder. Continue this process until the quotient becomes 0. Now, we write the remainders upside down to get the binary equivalent of 156, 10011100.
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., 2^7, 2^6, 2^5, and so on. Find the largest power that fits into 156. 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 156, we use 0s for 2^6, 2^5, 2^1, and 2^0 and 1s for 2^7, 2^4, 2^3, and 2^2.
Tips and Tricks for Binary Numbers till 156
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 156.
Memorize to speed up conversions: We can memorize the binary forms for numbers with common patterns. 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, 156 is even, and its binary form is 10011100. Here, the binary of 156 ends in 0. If the number is odd, then its binary equivalent will end in 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 156 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, 156 can be mistakenly written as 11001100 instead of 10011100.
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 156 and 2 instead of dividing 156 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.
156 in Binary Examples
Problem 1
Convert 156 from decimal to binary using the place value method.
10011100
Explanation
2^7 is the largest power of 2, which is less than or equal to 156. So place 1 next to 2^7. Subtracting 128 from 156, we get 28. So the next largest power would be 2^4. So place another 1 next to 2^4. Now, subtracting 16 from 28, we get 12. Next, place 1 next to 2^3 and 2^2 after subtracting the corresponding values. By using this method, we can find the binary form of 156.
Problem 2
Convert 156 from decimal to binary using the division by 2 method.
10011100
Explanation
Divide 156 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 156 to binary using the representation method.
10011100
Explanation
Break the number 156 into powers of 2 and find the largest powers of 2. We get 2^7. So 1 is placed next to 2^7. Next, 156 - 128 = 28. Now, the largest power of 2 is 2^4. Once again, 1 is placed next to 2^4. Continue the process until the remainder is 0. After getting 0, fill in with zeros for unused powers of 2. By following this method, we get the binary value of 156 as 10011100.
Problem 4
How is 156 written in decimal, octal, and binary form?
Decimal form - 156 Octal - 234 Binary - 10011100
Explanation
The decimal system is also called the base 10 system. In this system, 156 is written as 156 only. We have already seen how 156 is written as 10011100 in binary. So, let us focus on the octal system, which is base 8. To convert 156 to octal, we need to divide 156 by 8. So 156 / 8 = 19 with 4 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. Finally, 2 / 8 = 0 with 2 as the remainder. The division process stops here because the quotient is now 0. Here, 4, 3, and 2 are the remainders, and they have to be written in reverse order. So, 234 is the octal equivalent of 156.
Problem 5
Express 156 - 56 in binary.
1100100
Explanation
156 - 56 = 100 So, we need to write 100 in binary. Start by dividing 100 by 2. We get 50 as the quotient and 0 as the remainder. Next, divide 50 by 2. Now we get 25 as the quotient and 0 as the remainder. Divide 25 by 2 to get 12 as the quotient and 1 as the remainder. Continue this process until the quotient becomes 0. Now write the remainders from bottom to top to get 1100100 (binary of 100).
FAQs on 156 in Binary
1.What is 156 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 Australia use numbers in everyday life to understand 156 in Binary?
7.What are some fun ways kids in Australia can practice 156 in Binary with numbers?
8.What role do numbers and 156 in Binary play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve 156 in Binary skills?
Important Glossaries for 156 in Binary
- Decimal: It is the base 10 number system that 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 156 (base 10), 1 has occupied the hundreds place, 5 is in the tens place, and 6 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 the division of one number by another.
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.
