104 LearnersLast updated on August 21, 2025
12! in Binary
12! in binary represents the factorial of 12 converted into the binary number system, which 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 the conversion of 12! to a binary system.
12! in Binary Conversion
The process of converting 12! from decimal to binary involves first calculating 12! and then converting the result to binary. 12! (12 factorial) is the product of all positive integers up to 12.
Once we have the decimal value, we divide it by 2 to convert it to binary, using the quotient as the dividend in the next step, continuing until the quotient becomes 0.
In the final step, the remainders are noted down from bottom to top, which forms the binary equivalent. This is a commonly used method to convert large numbers like 12! to binary.
12! in Binary Chart
In the table shown below, the first column shows the binary digits obtained from converting 12!. The second column represents the place values of each binary 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 the binary result is indeed the decimal equivalent of 12!.
How to Write 12! in Binary
12! can be converted from decimal to binary using different methods. 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 12! using the expansion method.
Step 1 - Calculate 12!: The factorial of 12 is calculated as follows: 12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 479001600.
Step 2 - Convert 12! to binary: Now that we have the decimal value, we convert it to binary.
Step 3 - Identify the largest power of 2: Determine the powers of 2 for the binary representation.
Step 4 - Subtract and record 1s and 0s: Write 1 in the places where the power of 2 fits into 12!, and 0 where it doesn't.
Step 5 - Write the values in reverse order: We now write the numbers upside down to represent 12! in binary.
Grouping Method: In this method, we divide the decimal result of 12! by 2. Let us see the step-by-step conversion.
Step 1 - Divide the calculated factorial (479001600) by 2 and note the quotient and remainder.
Step 2 - Continue dividing the quotient by 2 until it becomes 0.
Step 3 - Write down the remainders from bottom to top. Therefore, the binary representation of 12! is achieved.
Rules for Binary Conversion of 12!
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 involves finding the largest power of 2. Let’s see a brief step-by-step explanation to understand the first rule. Calculate the factorial, 12! = 479001600. Find the largest power of 2 less than or equal to this factorial. Subtract the value from 12! and place 1s and 0s accordingly. Continue until the remainder becomes 0. Write the binary number from the remainders.
Rule 2: Division by 2 Method
The division by 2 method is similar to the grouping method. A brief step-by-step explanation is given below for better understanding. Divide the factorial by 2 to get the quotient and remainder. Repeat the process with the quotient until it becomes 0. Write the remainders upside down to obtain the binary equivalent.
Rule 3: Representation Method
This rule involves breaking the number into powers of 2. Identify the powers of 2 and write them down in decreasing order. Find the largest power that fits into 12!. Allocate 1s and 0s to the suitable powers of 2. Combine the digits 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.
Tips and Tricks for Binary Numbers till 12!
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 related to 12!.
Memorize to speed up conversions: We can memorize small binary numbers to aid in solving large ones like 12!. Recognize the patterns: Converting numbers from decimal to binary follows a pattern.
Even and odd rule: Whenever a number is even, its binary form will end in 0. If odd, it ends in 1.
Cross-verify the answers: Once the conversion is done, cross-verify by converting back to decimal.
Practice by using tables: Writing decimal numbers and their binary equivalents in a table helps remember conversions.
Common Mistakes and How to Avoid Them in 12! 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, be careful while representing any number in its binary form. For large numbers like 12!, misplaced digits can lead to errors.
Mistake 3
Not Practicing Enough
Converting numbers from decimal to binary regularly will help boost our confidence and minimize mistakes. Practice daily to become proficient in converting numbers to binary.
Mistake 4
Adding Instead of Dividing
When using the grouping method, students may incorrectly add instead of dividing when converting large numbers like 12! by 2. Always remember to use division 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.
12! in Binary Examples
Problem 1
Convert 12! from decimal to binary using the place value method.
The binary equivalent of 12! is a lengthy binary number that results from these calculations.
Explanation
First, calculate 12! = 479001600. Identify the largest power of 2 less than or equal to this number. Subtract each power of 2 from 12! and write 1 for each used power. Continue until the remainder is 0, filling in 0s for unused powers.
Problem 2
Convert 12! from decimal to binary using the division by 2 method.
The binary equivalent of 12! is achieved by repeated divisions.
Explanation
Divide 479001600 by 2. Use the quotient as the new dividend and continue dividing until the quotient is 0. Write the remainders upside down to get the binary representation of 12!.
Problem 3
Convert 12! to binary using the representation method.
The binary equivalent of 12! is a result of powers of 2.
Explanation
Break 12! into powers of 2. Allocate 1s and 0s to each power, starting from the largest that fits into 479001600, down to 0. This process yields the binary value.
Problem 4
How is 12! written in decimal, octal, and binary form?
Decimal form - 479001600 Octal - Equivalent octal representation Binary - Equivalent binary representation
Explanation
The decimal system is base 10, so 12! is calculated directly. Converting to octal involves dividing by 8 repeatedly. The binary form is obtained by dividing by 2 repeatedly.
Problem 5
Express 12! - 479001595 in binary.
101
Explanation
12! - 479001595 = 5 So, we need to write 5 in binary. Start by dividing 5 by 2, which gives 2 as the quotient and 1 as the remainder. Next, divide 2 by 2, which gives 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 101 (binary of 5).
FAQs on 12! in Binary
1.What is 12! 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 12! in Binary?
7.What are some fun ways kids in United States can practice 12! in Binary with numbers?
8.What role do numbers and 12! 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 12! in Binary skills?
Important Glossaries for 12! in Binary
- Factorial: The product of all positive integers up to a given number, denoted by n!.
- 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.
- Decimal: It is the base 10 number system which uses digits from 0 to 9.
- Octal: It is the number system with a base of 8. It uses digits from 0 to 7.
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.
