109 LearnersLast updated on August 21, 2025
1143 in Binary
1143 in binary is written as 10001110111 because the binary system uses only two digits, 0 and 1, to represent numbers. This numbering system is widely used in computer systems. In this topic, we are going to learn about the binary representation of 1143.
1143 in Binary Conversion
The process of converting 1143 from decimal to binary involves dividing the number 1143 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 1143 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 1143 by 2 until getting 0 as the quotient result in 10001110111. Remember, the remainders here have been written upside down.
1143 in Binary Chart
In the table shown below, the first column shows the binary digits (1 and 0) as 10001110111.
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 10001110111 in binary is indeed 1143 in the decimal number system.
How to Write 1143 in Binary
1143 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 1143 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 2^9 = 512 2^10= 1024 Since 2048 is greater than 1143, we stop at 2^10 = 1024.
Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2^10 = 1024. 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, 1143. Since 2^10 is the number we are looking for, write 1 in the 2^10 place. Now the value of 2^10, which is 1024, is subtracted from 1143. 1143 - 1024 = 119.
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, 119. So, the next largest power of 2 is 2^6, which is less than or equal to 119. Now, we have to write 1 in the 2^6 places. And then subtract 64 from 119. 119 - 64 = 55.
Step 4 - Continue identifying the next largest powers: We continue this process, identifying the next largest power of 2 that fits into the result from the previous step until the remainder is 0. 55 - 32 = 23 (write 1 in the 2^5 place) 23 - 16 = 7 (write 1 in the 2^4 place) 7 - 4 = 3 (write 1 in the 2^2 place) 3 - 2 = 1 (write 1 in the 2^1 place) 1 - 1 = 0 (write 1 in the 2^0 place)
Step 5 - Identify the unused place values: In the steps above, we wrote 1s in the 2^10, 2^6, 2^5, 2^4, 2^2, 2^1, and 2^0 places. Now, we can just write 0s in the remaining places, which are 2^9, 2^8, 2^7, and 2^3. Now, by substituting the values, we get, 0 in the 2^9 place 0 in the 2^8 place 0 in the 2^7 place 1 in the 2^6 place 1 in the 2^5 place 1 in the 2^4 place 0 in the 2^3 place 1 in the 2^2 place 1 in the 2^1 place 1 in the 2^0 place
Step 6 - Write the values in reverse order: We now write the numbers upside down to represent 1143 in binary. Therefore, 10001110111 is 1143 in binary.
Grouping Method: In this method, we divide the number 1143 by 2. Let us see the step-by-step conversion.
Step 1 - Divide the given number 1143 by 2. 1143 / 2 = 571. Here, 571 is the quotient and 1 is the remainder.
Step 2 - Divide the previous quotient (571) by 2. 571 / 2 = 285. Here, the quotient is 285 and the remainder is 1.
Step 3 - Repeat the previous step. 285 / 2 = 142. Now, the quotient is 142, and 1 is the remainder.
Step 4 - Repeat the previous step. 142 / 2 = 71. Here, the quotient is 71 and the remainder is 0.
Step 5 - Repeat the previous step. 71 / 2 = 35. Here, the quotient is 35 and the remainder is 1.
Step 6 - Repeat the previous step. 35 / 2 = 17. Here, the quotient is 17 and the remainder is 1.
Step 7 - Repeat the previous step. 17 / 2 = 8. Here, the quotient is 8 and the remainder is 1.
Step 8 - Repeat the previous step. 8 / 2 = 4. Here, the quotient is 4 and the remainder is 0.
Step 9 - Repeat the previous step. 4 / 2 = 2. Here, the quotient is 2 and the remainder is 0.
Step 10 - Repeat the previous step. 2 / 2 = 1. Here, the quotient is 1 and the remainder is 0.
Step 11 - Repeat the previous step. 1 / 2 = 0. Here, the remainder is 1. And we stop the division here because the quotient is 0.
Step 12 - Write down the remainders from bottom to top. Therefore, 1143 (decimal) = 10001110111 (binary).
Rules for Binary Conversion of 1143
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 1143. Since the answer is 2^10, write 1 next to this power of 2. Subtract the value (1024) from 1143. So, 1143 - 1024 = 119. Find the largest power of 2 less than or equal to 119. The answer is 2^6. So, write 1 next to this power. Continue this process until the remainder is 0. Now, write 0 next to the remaining powers. Final conversion will be 10001110111.
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, 1143 is divided by 2 to get 571 as the quotient and 1 as the remainder. Now, 571 is divided by 2. Here, we will get 285 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 1143, 10001110111.
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., 2^10, 2^9, 2^8, ..., 2^0. Find the largest power that fits into 1143. 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 1143, we use 0s for 2^9, 2^8, 2^7, and 2^3 and 1s for other relevant powers of 2.
Tips and Tricks for Binary Numbers till 1143
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 1143.
Memorize to speed up conversions: We can memorize the binary forms for smaller numbers to assist with larger 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, 1142 is even and its binary form ends in 0. If the number is odd, then its binary equivalent will end in 1. For example, the binary of 1143 (an odd number) is 10001110111. 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 1143 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, 1143 can be mistakenly written as 11010111011 instead of 10001110111.
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 1143 and 2 instead of dividing 1143 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.
1143 in Binary Examples
Problem 1
Convert 1143 from decimal to binary using the place value method.
10001110111
Explanation
2^10 is the largest power of 2, which is less than or equal to 1143. So place 1 next to 2^10. Subtracting 1024 from 1143, we get 119. So the next largest power would be 2^6. So place another 1 next to 2^6. Continue this process for the remaining numbers until the remainder is 0. By using this method, we can find the binary form of 1143.
Problem 2
Convert 1143 from decimal to binary using the division by 2 method.
10001110111
Explanation
Divide 1143 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 1143 to binary using the representation method.
10001110111
Explanation
Break the number 1143 into powers of 2 and find the largest powers of 2. We get 2^10. So 1 is placed next to 2^10. Next, 1143 - 1024 = 119. Now, the largest power of 2 is 2^6. Once again, 1 is placed next to 2^6. Continue this 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 1143 as 10001110111.
Problem 4
How is 1143 written in decimal, octal, and binary form?
Decimal form - 1143 Octal - 2177 Binary - 10001110111
Explanation
The decimal system is also called the base 10 system. In this system, 1143 is written as 1143 only. We have already seen how 1143 is written as 10001110111 in binary. So, let us focus on the octal system, which is base 8. To convert 1143 to octal, we need to divide 1143 by 8. So 1143 / 8 = 142 with 7 as the remainder. In the next step, divide the quotient from the previous step (142) by 8. So 142 / 8 = 17 with 6 as the remainder. Then, divide the next quotient (17) by 8. So 17 / 8 = 2 with 1 as the remainder. Finally, divide 2 by 8 to get 0 with 2 as the remainder. The division process stops here because the quotient is now 0. Here, 7, 6, 1, and 2 are the remainders, and they have to be written in reverse order. So, 2177 is the octal equivalent of 1143.
Problem 5
Express 1143 - 543 in binary.
100110000
Explanation
1143 - 543 = 600 So, we need to write 600 in binary. Start by dividing 600 by 2. We get 300 as the quotient and 0 as the remainder. Next, divide 300 by 2. Now we get 150 as the quotient and 0 as the remainder. Divide 150 by 2 to get 75 as the quotient and 0 as the remainder. Divide 75 by 2 to get 37 as the quotient and 1 as the remainder. Divide 37 by 2 to get 18 as the quotient and 1 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. 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 100110000 (binary of 600).
FAQs on 1143 in Binary
1.What is 1143 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 States use numbers in everyday life to understand 1143 in Binary?
7.What are some fun ways kids in United States can practice 1143 in Binary with numbers?
8.What role do numbers and 1143 in Binary play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve 1143 in Binary skills?
Important Glossaries for 1143 in Binary
- Decimal: 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 1143 (base 10), 1 has occupied the thousands place, 1 is in the hundreds place, 4 is in the tens place, and 3 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 a mathematical operation. For example, when dividing 1143 by 2, the quotient is the result of each division step.
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.
