102 LearnersLast updated on 17 August 2025
10010 in Binary
10010 in binary is a representation of the decimal number 18. In this topic, we will explore how to convert decimal numbers to binary, focusing on the example of 18, which is written as 10010 in the binary system. The binary system uses only two digits, 0 and 1, to represent numbers and is crucial in computing.
18 in Binary Conversion
The process of converting 18 from decimal to binary involves dividing the number 18 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.
For example, the remainders noted after dividing 18 by 2 until getting 0 as the quotient is 10010. Remember, the remainders are recorded from bottom to top to get the correct binary value.
18 in Binary Chart
In the table shown below, the first column represents the binary digits (1 and 0) for 18. The second column shows 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 verify that 10010 in binary is indeed 18 in the decimal number system.
How to Write 18 in Binary
18 can be converted from decimal to binary using various methods. Here are two common methods:
Expansion Method:
Step 1 - Determine the place values: In the binary system, each place value is a power of 2. Therefore, we will identify the powers of 2. 20 = 1 21 = 2 22 = 4 23 = 8 24 = 16 25 = 32 Since 32 is greater than 18, we stop at 24 = 16.
Step 2 - Identify the largest power of 2: We stopped at 24 = 16, as it is the largest power of 2 less than or equal to 18. Write 1 in the 24 place. Now subtract 16 from 18. 18 - 16 = 2
Step 3 - Identify the next largest power of 2: The largest power of 2 that fits into the result of the previous step, 2, is 21. Write 1 in the 21 place. Then subtract 2 from 2. 2 - 2 = 0. Stop here as the remainder is 0.
Step 4 - Identify unused place values: Write 0s in the remaining places, which are 20, 22, and 23.
Step 5 - Write the values in reverse order: We now write the numbers upside down to represent 18 in binary. Therefore, 10010 is 18 in binary.
Grouping Method:
Step 1 - Divide 18 by 2. 18 / 2 = 9. Here, 9 is the quotient, and 0 is the remainder.
Step 2 - Divide the previous quotient (9) by 2. 9 / 2 = 4. The quotient is 4, and the remainder is 1.
Step 3 - Repeat the previous step. 4 / 2 = 2. Now, the quotient is 2, and 0 is the remainder.
Step 4 - Repeat the previous step. 2 / 2 = 1. The quotient is 1, and the remainder is 0.
Step 5 - Repeat the previous step. 1 / 2 = 0. Here, the remainder is 1. Stop as the quotient is 0.
Step 6 - Write down the remainders from bottom to top. Therefore, 18 (decimal) = 10010 (binary).
Rules for Binary Conversion of 18
When converting numbers to binary, follow these rules:
Rule 1: Place Value Method
Find the largest power of 2 less than or equal to the number. Write 1 next to this power of 2. Subtract the value from the original number. Repeat the process for the remainder. Write 0s for unused powers of 2. The final conversion will be 10010 for 18.
Rule 2: Division by 2 Method
Divide the number by 2 repeatedly. Record the remainders. Stop when the quotient is 0. Write the remainders in reverse order.
Rule 3: Representation Method
Identify powers of 2 and write them in decreasing order: 24, 23, 22, etc. Find the largest power that fits into the number. Repeat the process, allocating 1s and 0s appropriately. Combine the digits to get the binary result.
Rule 4: Limitation Rule
The binary system uses only 0s and 1s to represent numbers. This is a base 2 system, where each binary place represents a power of 2.
Tips and Tricks for Binary Numbers till 18
Here are some tips and tricks for working with binary numbers up to 18:
- Memorize conversions: Memorizing binary forms for numbers 1 to 18 can speed up conversions. 1 → 1, 2 → 10, 3 → 11, 4 → 100, 5 → 101, 6 → 110, 7 → 111, 8 → 1000, 9 → 1001, 10 → 1010, 11 → 1011, 12 → 1100, 13 → 1101, 14 → 1110, 15 → 1111, 16 → 10000, 17 → 10001, 18 → 10010.
- Recognize patterns: Notice patterns in binary conversion. Even numbers end with 0, odd numbers end with 1.
- Cross-verify answers: Convert the binary back to decimal to check for accuracy.
- Practice with tables: Writing tables of decimal numbers and their binary equivalents helps retention.
Common Mistakes and How to Avoid Them in 18 in Binary
Here are common mistakes people make when converting numbers to binary:
Mistake 1
Writing the Remainders From Top to Bottom
Always write remainders from bottom to top when using the division by 2 method for converting to binary.
Mistake 2
Misplacing 1s and 0s
Be careful to place 1s and 0s correctly.
For example, 18 can be mistakenly written as 10001 instead of 10010.
Mistake 3
Not Practicing Enough
Regular practice in converting numbers from decimal to binary will help minimize mistakes.
Mistake 4
Adding Instead of Dividing
Ensure division is used in the conversion process, not addition.
Mistake 5
Stopping the Division Too Early
Continue dividing until the quotient is 0 to avoid errors in the final calculation.
18 in Binary Examples
Problem 1
Convert 18 from decimal to binary using the place value method.
10010
Explanation
24 is the largest power of 2 less than or equal to 18.
So place 1 next to 24. Subtract 16 from 18 to get 2.
The next largest power is 21. Place another 1 next to 21.
Now, subtracting 2 from 2, we get 0.
Place 0s in the remaining powers of 2, which are 20, 22, and 23.
This method gives us the binary form of 18.
Problem 2
Convert 18 from decimal to binary using the division by 2 method.
10010
Explanation
Divide 18 by 2.
The quotient becomes the new dividend.
Continue until the quotient is 0.
Write the remainders upside down to get the final result.
Problem 3
Convert 18 to binary using the representation method.
10010
Explanation
Break down 18 into powers of 2.
The largest powers fitting 18 are 24 and 21.
Subtract 16 from 18 to get 2, then subtract 2 from 2 to get 0.
Fill in zeros for unused powers of 2.
The binary value of 18 is 10010.
Problem 4
How is 18 written in decimal, octal, and binary form?
Decimal form - 18 Octal - 22 Binary - 10010
Explanation
The decimal system is base 10, so 18 is written as 18.
We've already seen 18 as 10010 in binary.
For octal (base 8), divide 18 by 8 to get 2 with a remainder of 2.
So, 22 is the octal equivalent of 18.
Problem 5
Express 18 - 5 in binary.
1101
Explanation
18 - 5 = 13 Write 13 in binary:
Divide 13 by 2 to get 6 as the quotient and 1 as the remainder.
Divide 6 by 2 to get 3 as the quotient and 0 as the remainder.
Divide 3 by 2 to get 1 as the quotient and 1 as the remainder.
Divide 1 by 2 to get 0 as the quotient and 1 as the remainder.
Write the remainders from bottom to top to get 1101 (binary of 13).
FAQs on 18 in Binary
1.What is 18 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 10010 in Binary?
7.What are some fun ways kids in Australia can practice 10010 in Binary with numbers?
8.What role do numbers and 10010 in Binary play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve 10010 in Binary skills?
Important Glossaries for 18 in Binary
- Decimal: A base 10 number system using digits 0 to 9.
- Binary: A base 2 number system using digits 0 and 1.
- Place value: The value of a digit based on its position in a number.
- Octal: A base 8 number system using digits 0 to 7.
- Quotient: The result of division in arithmetic.
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.
