106 LearnersLast updated on August 18th, 2025
83 in Binary
83 in binary is written as 1010011 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 the conversion of 83 into binary.
83 in Binary Conversion
The process of converting 83 from decimal to binary involves dividing the number 83 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 83 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 83 by 2 until getting 0 as the quotient is 1010011. Remember, the remainders here have been written upside down.
83 in Binary Chart
In the table shown below, the first column shows the binary digits (1 and 0) as 1010011. 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 1010011 in binary is indeed 83 in the decimal number system.
How to Write 83 in Binary
83 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 83 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 Since 64 is less than 83, we start with 2^6 = 64.
Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2^6 = 64. 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, 83. Since 2^6 is the number we are looking for, write 1 in the 2^6 place. Now the value of 2^6, which is 64, is subtracted from 83. 83 - 64 = 19.
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, 19. So, the next largest power of 2 is 2^4, which is less than or equal to 19. Now, we have to write 1 in the 2^4 place. And then subtract 16 from 19. 19 - 16 = 3.
Step 4 - Identify the next largest power of 2: Now, the largest power of 2 that fits into 3 is 2^1. Write 1 in the 2^1 place. And then subtract 2 from 3. 3 - 2 = 1.
Step 5 - Identify the next largest power of 2: Finally, 2^0 is the largest power of 2 that fits into 1. Write 1 in the 2^0 place. And then subtract 1 from 1. 1 - 1 = 0. We need to stop the process here since the remainder is 0.
Step 6 - Identify the unused place values: In the steps above, we wrote 1 in the 2^6, 2^4, 2^1, and 2^0 places. Now, we can just write 0s in the remaining places, which are 2^5, 2^3, and 2^2. Now, by substituting the values, we get, 1 in the 2^6 place 0 in the 2^5 place 1 in the 2^4 place 0 in the 2^3 place 0 in the 2^2 place 1 in the 2^1 place 1 in the 2^0 place
Step 7 - Write the values in reverse order: We now write the numbers upside down to represent 83 in binary. Therefore, 1010011 is 83 in binary.
Grouping Method: In this method, we divide the number 83 by 2. Let us see the step-by-step conversion.
Step 1 - Divide the given number 83 by 2. 83 / 2 = 41. Here, 41 is the quotient, and 1 is the remainder.
Step 2 - Divide the previous quotient (41) by 2. 41 / 2 = 20. Here, the quotient is 20 and the remainder is 1.
Step 3 - Repeat the previous step. 20 / 2 = 10. Now, the quotient is 10, and 0 is the remainder.
Step 4 - Repeat the previous step. 10 / 2 = 5. Here, the quotient is 5, and 0 is the remainder.
Step 5 - Repeat the previous step. 5 / 2 = 2. Here, the quotient is 2, and 1 is the remainder.
Step 6 - Repeat the previous step. 2 / 2 = 1. Here, the quotient is 1, and 0 is the remainder.
Step 7 - Repeat the previous step. 1 / 2 = 0. Here, the quotient is 0, and 1 is the remainder. And we stop the division here because the quotient is 0.
Step 8 - Write down the remainders from bottom to top. Therefore, 83 (decimal) = 1010011 (binary).
Rules for Binary Conversion of 83
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 83. Since the answer is 26, write 1 next to this power of 2. Subtract the value (64) from 83. So, 83 - 64 = 19. Find the largest power of 2 less than or equal to 19. The answer is 24. So, write 1 next to this power. Now, 19 - 16 = 3. Find the largest power of 2 less than or equal to 3. The answer is 21. So, write 1 next to this power. Now, 3 - 2 = 1. Find the largest power of 2 less than or equal to 1. The answer is 20. So, write 1 next to this power. Since there is no remainder, we can write 0 next to the remaining powers (25, 23, and 22). Final conversion will be 1010011.
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, 83 is divided by 2 to get 41 as the quotient and 1 as the remainder. Now, 41 is divided by 2. Here, we will get 20 as the quotient and 1 as the remainder. Dividing 20 by 2, we get 10 as the quotient and 0 as the remainder. Divide 10 by 2 to get 5 as the quotient and 0 as the remainder. Divide 5 by 2 to get 2 as the quotient and 1 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. We stop the division once the quotient becomes 0. Now, we write the remainders upside down to get the binary equivalent of 83, which is 1010011.
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., 26, 25, 24, 23, 22, 21, and 20. Find the largest power that fits into 83. 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 83, we use 0s for 25, 23, and 22 and 1s for 26, 24, 21, and 20.
Tips and Tricks for Binary Numbers till 83
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 83.
Memorize to speed up conversions: We can memorize the binary forms for numbers 1 to 83. 1 → 1, 2 → 10, 3 → 11, 4 → 100, 5 → 101, 6 → 110, 7 → 111, 8 → 1000, 9 → 1001, 10 → 1010, 11 → 1011, ..., 83 → 1010011.
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, 82 is even, and its binary form is 1010010. Here, the binary of 82 ends in 0. If the number is odd, then its binary equivalent will end in 1. For example, the binary of 83 (an odd number) is 1010011. 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 83 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, 83 can be mistakenly written as 1100101 instead of 1010011.
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 83 and 2 instead of dividing 83 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.
83 in Binary Examples
Problem 1
Convert 83 from decimal to binary using the place value method.
1010011
Explanation
26 is the largest power of 2, which is less than or equal to 83. So place 1 next to 2^6. Subtracting 64 from 83, we get 19. The next largest power would be 24. So place another 1 next to 24.
Next, subtracting 16 from 19, we get 3. The next largest power would be 21. So place another 1 next to 21. Finally, subtracting 2 from 3, we get 1.
So the next largest power would be 20. Place another 1 next to 20. By using this method, we can find the binary form of 83.
Problem 2
Convert 83 from decimal to binary using the division by 2 method.
1010011
Explanation
Divide 83 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 83 to binary using the representation method.
1010011
Explanation
Break the number 83 into powers of 2 and find the largest powers of 2. We get 26. So 1 is placed next to 26. Next, 83 - 64 = 19. Now, the largest power of 2 is 24. Once again, 1 is placed next to 24. Then, 19 - 16 = 3. The largest power of 2 is 21. Place 1 next to 21. Finally, 3 - 2 = 1. The largest power of 2 is 20. Place 1 next to 20. After getting 0, fill in with zeros for unused powers of 2. By following this method, we get the binary value of 83 as 1010011.
Problem 4
How is 83 written in decimal, octal, and binary form?
Decimal form - 83 Octal - 123 Binary - 1010011
Explanation
The decimal system is also called the base 10 system. In this system, 83 is written as 83 only. We have already seen how 83 is written as 1010011 in binary. So, let us focus on the octal system, which is base 8. To convert 83 to octal, we need to divide 83 by 8. So 83 / 8 = 10 with 3 as the remainder.
In the next step, divide the quotient from the previous step (10) by 8. So 10 / 8 = 1 with 2 as the remainder. The division process stops here because the quotient is now 0. Here, 2, 3, and 1 are the remainders, and they have to be written in reverse order. So, 123 is the octal equivalent of 83.
Problem 5
Express 83 - 37 in binary.
101100
Explanation
83 - 37 = 46 So, we need to write 46 in binary. Start by dividing 46 by 2. We get 23 as the quotient and 0 as the remainder. Next, divide 23 by 2. Now we get 11 as the quotient and 1 as the remainder. Divide 11 by 2 to get 5 as the quotient and 1 as the remainder. Divide 5 by 2 to get 2 as the quotient and 1 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 101100 (binary of 46).
FAQs on 83 in Binary
1.What is 83 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 83 in Binary?
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8.What role do numbers and 83 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 83 in Binary skills?
Important Glossaries for 83 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 occupies 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: Each position in a binary number represents a power of 2, starting from 20 on the right. ```
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.
