1200 in Binary

The process of converting 1200 from decimal to binary involves dividing the number 1200 by 2. Here, it is getting 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 1200 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 1200 by 2 until getting 0 as the quotient is 10010110000. Remember, the remainders here have been written upside down.

In the table shown below, the first column shows the binary digits (1 and 0) as 10010110000.

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 10010110000 in binary is indeed 1200 in the decimal number system.

1200 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 1200 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 1024 is less than 1200, we stop at 2^10 = 1024.

Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2^10 = 1024. In this step, we have to identify the largest power of 2, which is less than or equal to the given number, 1200. 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 1200. 1200 - 1024 = 176.

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, 176. So, the next largest power of 2 is 2^7, which is 128. Now, we have to write 1 in the 2^7 place. And then subtract 128 from 176. 176 - 128 = 48.

Step 4 - Repeat the process: Continue identifying the largest power of 2 less than or equal to the remainder. The next largest power is 2^5 = 32. Write 1 in the 2^5 place and subtract 32 from 48. 48 - 32 = 16.

Step 5 - Continue until remainder is 0: Find the largest power of 2 that fits into the current remainder. 2^4 = 16 fits perfectly. 16 - 16 = 0. We need to stop the process here since the remainder is 0.

Step 6 - Identify the unused place values: In the previous steps, we wrote 1 in the 2^10, 2^7, 2^5, and 2^4 places. Now, we can just write 0s in the remaining places. Now, by substituting the values, we get, 0 in the 2^0 place 0 in the 2^1 place 0 in the 2^2 place 0 in the 2^3 place 1 in the 2^4 place 0 in the 2^5 place 1 in the 2^6 place 1 in the 2^7 place 0 in the 2^8 place 0 in the 2^9 place 1 in the 2^10 place

Step 7 - Write the values in reverse order: We now write the numbers upside down to represent 1200 in binary. Therefore, 10010110000 is 1200 in binary.

Grouping Method: In this method, we divide the number 1200 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 1200 by 2. 1200 / 2 = 600. Here, 600 is the quotient and 0 is the remainder.

Step 2 - Divide the previous quotient (600) by 2. 600 / 2 = 300. Here, the quotient is 300 and the remainder is 0.

Step 3 - Repeat the previous step. 300 / 2 = 150. Now, the quotient is 150 and 0 is the remainder.

Step 4 - Repeat the previous step. 150 / 2 = 75. Here, the remainder is 0.

Step 5 - Continue dividing by 2 until the quotient becomes 0. 75 / 2 = 37 remainder 1 37 / 2 = 18 remainder 1 18 / 2 = 9 remainder 0 9 / 2 = 4 remainder 1 4 / 2 = 2 remainder 0 2 / 2 = 1 remainder 0 1 / 2 = 0 remainder 1

Step 6 - Write down the remainders from bottom to top. Therefore, 1200 (decimal) = 10010110000 (binary).

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 1200. Since the answer is 2^10, write 1 next to this power of 2. Subtract the value (1024) from 1200. So, 1200 - 1024 = 176. Find the largest power of 2 less than or equal to 176. The answer is 2^7. So, write 1 next to this power. Now, 176 - 128 = 48. Continue the process until the remainder is 0. Final conversion will be 10010110000.

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, 1200 is divided by 2 to get 600 as the quotient and 0 as the remainder. Now, 600 is divided by 2. Here, we will get 300 as the quotient and 0 as the remainder. Continue dividing the quotient by 2. We stop the division once the quotient becomes 0. Now, we write the remainders upside down to get the binary equivalent of 1200, 10010110000.

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 1200. 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 1200, we use 0s for unused powers of 2 and 1s where applicable.

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 1200.

Memorize to speed up conversions: We can memorize the binary forms for numbers like powers of 2 and their combinations. 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 Understand powers of 2 and their binary representation, which helps in quick conversions.

Even and odd rule: Whenever a number is even, its binary form will end in 0. For example, 1200 is even, and its binary form is 10010110000. If the number is odd, then its binary equivalent will end in 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.

• 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 a base 2 number system.

• Place value: Every digit has a value based on its position in a given number. For example, in 1200 (base 10), 1 has occupied the thousands place, 2 is in the hundreds place, and so on.

• Octal: It is the number system with a base of 8. It uses digits from 0 to 7.

• Power of 2: Each digit in a binary number represents a power of 2, which determines its value based on its position.