107 LearnersLast updated on August 19th, 2025
172 in Binary
172 in binary is written as 10101100 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 the number 172 to binary.
172 in Binary Conversion
The process of converting 172 from decimal to binary involves dividing the number 172 by 2. Here, it is continuously 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 172 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 172 by 2 until getting 0 as the quotient is 10101100. Remember, the remainders here have been written upside down.
172 in Binary Chart
In the table shown below, the first column shows the binary digits as 10101100. 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 10101100 in binary is indeed 172 in the decimal number system.
How to Write 172 in Binary
172 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 172 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 2^8 = 256 Since 256 is greater than 172, we stop at 2^7 = 128.
Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2^7 = 128, which is the largest power of 2 less than or equal to the given number, 172. 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 172. 172 - 128 = 44.
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, 44. So, the next largest power of 2 is 2^5, which is 32. Write 1 in the 2^5 place. Then subtract 32 from 44. 44 - 32 = 12.
Step 4 - Continue the process: Now find the largest power of 2 that fits into 12, which is 2^3 = 8. Write 1 in the 2^3 place. Subtract 8 from 12. 12 - 8 = 4.
Step 5 - Repeat for the remaining number: The largest power of 2 that fits into 4 is 2^2 = 4. Write 1 in the 2^2 place. Subtract 4 from 4. 4 - 4 = 0. We stop here since the remainder is 0.
Step 6 - Identify the unused place values: In the steps above, we wrote 1 in the 2^7, 2^5, 2^3, and 2^2 places. Now, write 0s in the remaining places, which are 2^6, 2^4, and 2^1. 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 0 in the 2^4 place 1 in the 2^5 place 0 in the 2^6 place 1 in the 2^7 place
Step 7 - Write the values in reverse order: We write the numbers upside down to represent 172 in binary. Therefore, 10101100 is 172 in binary.
Grouping Method: In this method, we divide the number 172 by 2. Let us see the step-by-step conversion.
Step 1 - Divide the given number 172 by 2. 172 / 2 = 86. Here, 86 is the quotient and 0 is the remainder.
Step 2 - Divide the previous quotient (86) by 2. 86 / 2 = 43. Here, the quotient is 43 and the remainder is 0.
Step 3 - Repeat the previous step. 43 / 2 = 21. Now, the quotient is 21, and 1 is the remainder.
Step 4 - Continue the process. 21 / 2 = 10. Quotient is 10, remainder is 1. 10 / 2 = 5. Quotient is 5, remainder is 0. 5 / 2 = 2. Quotient is 2, remainder is 1. 2 / 2 = 1. Quotient is 1, remainder is 0.
Step 5 - Repeat the previous step. 1 / 2 = 0. Here, the remainder is 1. We stop the division here because the quotient is 0. Step 6 - Write down the remainders from bottom to top.
Therefore, 172 (decimal) = 10101100 (binary).
Rules for Binary Conversion of 172
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 172. Since the answer is 2^7, write 1 next to this power of 2. Subtract the value (128) from 172. So, 172 - 128 = 44. Find the largest power of 2 less than or equal to 44. The answer is 2^5. So, write 1 next to this power. Now, 44 - 32 = 12. Find the largest power of 2 less than or equal to 12. The answer is 2^3. So, write 1 next to this power. Now, 12 - 8 = 4. Find the largest power of 2 less than or equal to 4. The answer is 2^2. So, write 1 next to this power. 4 - 4 = 0. Since there is no remainder, we write 0 next to the remaining powers (2^6, 2^4, and 2^1). Final conversion will be 10101100.
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, 172 is divided by 2 to get 86 as the quotient and 0 as the remainder. Now, 86 is divided by 2. Here, we get 43 as the quotient and 0 as the remainder. Dividing 43 by 2, we get 21 as the quotient and 1 as the remainder. Continue dividing until the quotient becomes 0. Write the remainders upside down to get the binary equivalent of 172, 10101100.
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., 2^7, 2^6, 2^5, 2^4, 2^3, 2^2, 2^1, and 2^0. Find the largest power that fits into 172. 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 172, we use 0s for 2^6, 2^4, and 2^1 and 1s for 2^7, 2^5, 2^3, and 2^2.
Tips and Tricks for Binary Numbers up to 172
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 172. Memorize to speed up conversions: We can memorize the binary forms for numbers 1 to 172.
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, 172 is even, and its binary form is 10101100. Here, the binary of 172 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 on a table will help us remember the conversions.
Common Mistakes and How to Avoid Them in 172 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, 172 can be mistakenly written as 1101100 instead of 10101100.
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 172 and 2 instead of dividing 172 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.
172 in Binary Examples
Problem 1
Convert 172 from decimal to binary using the place value method.
10101100
Explanation
2^7 is the largest power of 2, which is less than or equal to 172. So place 1 next to 2^7. Subtracting 128 from 172, we get 44. The next largest power would be 2^5. So place another 1 next to 2^5. Now, subtracting 32 from 44, we get 12. The next largest power is 2^3. So place another 1 next to 2^3. Now, subtracting 8 from 12, we get 4. The next largest power is 2^2. So place another 1 next to 2^2. Now, subtracting 4 from 4, we get 0. Now, just place 0s in the remaining powers of 2, which are 2^6, 2^4, and 2^1. By using this method, we can find the binary form of 172.
Problem 2
Convert 172 from decimal to binary using the division by 2 method.
10101100
Explanation
Divide 172 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 172 to binary using the representation method.
10101100
Explanation
Break the number 172 into powers of 2 and find the largest powers of 2. We get 2^7. So 1 is placed next to 2^7. Next, 172 - 128 = 44. Now, the largest power of 2 is 2^5. Once again, 1 is placed next to 2^5. Now, 44 - 32 = 12. The next largest power is 2^3. So place another 1 next to 2^3. Now, 12 - 8 = 4. The next largest power is 2^2. So place another 1 next to 2^2. Now, 4 - 4 = 0. After getting 0, fill in with zeros for unused powers of 2. By following this method, we get the binary value of 172 as 10101100.
Problem 4
How is 172 written in decimal, octal, and binary form?
Decimal form - 172 Octal - 254 Binary - 10101100
Explanation
The decimal system is also called the base 10 system. In this system, 172 is written as 172 only. We have already seen how 172 is written as 10101100 in binary. So, let us focus on the octal system, which is base 8. To convert 172 to octal, we need to divide 172 by 8. So 172 / 8 = 21 with 4 as the remainder. In the next step, divide the quotient from the previous step (21) by 8. So 21 / 8 = 2 with 5 as the remainder. In the final step, divide the quotient (2) by 8. So 2 / 8 = 0 with 2 as the remainder. The division process stops here because the quotient is now 0. Here, 4, 5, and 2 are the remainders, and they have to be written in reverse order. So, 254 is the octal equivalent of 172.
Problem 5
Express 172 - 5 in binary.
10100111
Explanation
172 - 5 = 167 So, we need to write 167 in binary. Start by dividing 167 by 2. We get 83 as the quotient and 1 as the remainder. Next, divide 83 by 2. Now we get 41 as the quotient and 1 as the remainder. Continue dividing until the quotient becomes 0. Write the remainders from bottom to top to get 10100111 (binary of 167).
FAQs on 172 in Binary
1.What is 172 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 Vietnam use numbers in everyday life to understand 172 in Binary?
7.What are some fun ways kids in Vietnam can practice 172 in Binary with numbers?
8.What role do numbers and 172 in Binary play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve 172 in Binary skills?
Important Glossaries for 172 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 102 (base 10), 1 has occupied the hundreds place, 0 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.
- Power of 2: In binary conversion, the place values are powers of 2, determining each digit's contribution to the total value.
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.
