111 LearnersLast updated on 21 August 2025
154 in Binary
154 in binary is written as 10011010 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 converting 154 to the binary system.
154 in Binary Conversion
The process of converting 154 from decimal to binary involves dividing the number 154 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 154 to binary. In the last step, the remainder is noted down from bottom to top, and that becomes the converted value.
For example, the remainders noted down after dividing 154 by 2 until getting 0 as the quotient is 10011010. Remember, the remainders here have been written upside down.
154 in Binary Chart
In the table shown below, the first column shows the binary digits (1 and 0) as 154.
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 10011010 in binary is indeed 154 in the decimal number system.
How to Write 154 in Binary
154 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 154 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 154, 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, 154. 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 154. 154 - 128 = 26.
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, 26. So, the next largest power of 2 is 2^4, which is less than or equal to 26. Now, we have to write 1 in the 2^4 places. And then subtract 16 from 26. 26 - 16 = 10.
Step 4 - Identify the next largest power of 2: Now, we need to find the largest power of 2 that fits into 10, which is 2^3. Write 1 in the 2^3 place and subtract 8 from 10. 10 - 8 = 2.
Step 5 - Identify the next largest power of 2: The next largest power of 2 that fits into 2 is 2^1. Write 1 in the 2^1 place and subtract 2 from 2. 2 - 2 = 0. We need to stop the process here since the remainder is 0.
Step 6 - Identify the unused place values: In step 2, step 3, step 4, and step 5, we wrote 1 in the 2^7, 2^4, 2^3, and 2^1 places. Now, we can just write 0s in the remaining places, which are 2^6, 2^5, 2^2, and 2^0. Now, by substituting the values, we get, 0 in the 2^0 place 1 in the 2^1 place 0 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 7 - Write the values in reverse order: We now write the numbers upside down to represent 154 in binary. Therefore, 10011010 is 154 in binary.
Grouping Method: In this method, we divide the number 154 by 2. Let us see the step-by-step conversion.
Step 1 - Divide the given number 154 by 2. 154 / 2 = 77. Here, 77 is the quotient and 0 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, 154 (decimal) = 10011010 (binary).
Rules for Binary Conversion of 154
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 154. Since the answer is 2^7, write 1 next to this power of 2. Subtract the value (128) from 154. So, 154 - 128 = 26. Find the largest power of 2 less than or equal to 26. The answer is 2^4. So, write 1 next to this power. Subtract 16 from 26, and then find the largest power of 2 less than or equal to the result (10). Continue this process until the remainder is 0. Final conversion will be 10011010.
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, 154 is divided by 2 to get 77 as the quotient and 0 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. Continue dividing the quotient by 2 until the quotient becomes 0. Now, we write the remainders upside down to get the binary equivalent of 154, 10011010.
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, etc. Find the largest power that fits into 154. 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 154, we use 1s for 2^7, 2^4, 2^3, and 2^1, and 0s for 2^6, 2^5, 2^2, and 2^0.
Tips and Tricks for Binary Numbers till 154
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.
Memorize to speed up conversions: We can memorize the binary forms for numbers.
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 153 (an odd number) is 10011001. 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 154 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, 154 can be mistakenly written as 10111010 instead of 10011010.
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 154 and 2 instead of dividing 154 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.
154 in Binary Examples
Problem 1
Convert 154 from decimal to binary using the place value method.
10011010
Explanation
2^7 is the largest power of 2, which is less than or equal to 154. So place 1 next to 2^7. Subtracting 128 from 154, we get 26. The next largest power is 2^4, so place another 1 next to 2^4. Subtracting 16 from 26, we get 10. The next largest power is 2^3, so place another 1 next to 2^3. Subtracting 8 from 10, we get 2. The next largest power is 2^1, so place another 1 next to 2^1. Now, subtracting 2 from 2, we get 0. Finally, place 0s in the remaining powers of 2, which are 2^6, 2^5, 2^2, and 2^0. By using this method, we can find the binary form of 154.
Problem 2
Convert 154 from decimal to binary using the division by 2 method.
10011010
Explanation
Divide 154 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 154 to binary using the representation method.
10011010
Explanation
Break the number 154 into powers of 2 and find the largest powers of 2. We get 2^7. So 1 is placed next to 2^7. Next, 154 - 128 = 26. Now, the largest power of 2 is 2^4. Once again, 1 is placed next to 2^4. Now, 26 - 16 = 10. The next largest power is 2^3, so 1 is placed next to 2^3. Now, 10 - 8 = 2. The next largest power is 2^1, so 1 is placed next to 2^1. Now, 2 - 2 = 0. After getting 0, fill in with zeros for unused powers of 2. By following this method, we get the binary value of 154 as 10011010.
Problem 4
How is 154 written in decimal, octal, and binary form?
Decimal form - 154 Octal - 232 Binary - 10011010
Explanation
The decimal system is also called the base 10 system. In this system, 154 is written as 154 only. We have already seen how 154 is written as 10011010 in binary. So, let us focus on the octal system, which is base 8. To convert 154 to octal, we need to divide 154 by 8. So 154 / 8 = 19 with 2 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, divide 2 by 8, which gives 0 as the quotient and 2 as the remainder. The division process stops here because the quotient is now 0. Here, 2, 3, and 2 are the remainders, and they have to be written in reverse order. So, 232 is the octal equivalent of 154.
Problem 5
Express 154 - 5 in binary.
10010011
Explanation
154 - 5 = 149 So, we need to write 149 in binary. Start by dividing 149 by 2. We get 74 as the quotient and 1 as the remainder. Next, divide 74 by 2. Now we get 37 as the quotient and 0 as the remainder. Divide 37 by 2 to get 18 as the quotient and 1 as the remainder. Continue this process: 18 by 2 gives 9 as the quotient and 0 as the remainder, 9 by 2 gives 4 as the quotient and 1 as the remainder, 4 by 2 gives 2 as the quotient and 0 as the remainder, and 2 by 2 gives 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. Now, write the remainders from bottom to top to get 10010011 (binary of 149).
FAQs on 154 in Binary
1.What is 154 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 India use numbers in everyday life to understand 154 in Binary?
7.What are some fun ways kids in India can practice 154 in Binary with numbers?
8.What role do numbers and 154 in Binary play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve 154 in Binary skills?
Important Glossaries for 154 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.
- Octal: It is the number system with a base of 8. It uses digits from 0 to 7.
- Hexadecimal: This number system has 16 digits. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. Here, A to F represent the values 10 to 15.
- 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.
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.
