2304 in Binary

The process of converting 2304 from decimal to binary involves dividing the number 2304 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 2304 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 2304 by 2 until getting 0 as the quotient is 100100000000. 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 100100000000.

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 100100000000 in binary is indeed 2304 in the decimal number system.

2304 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 2304 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. 2⁰ = 1 2¹ = 2 2² = 4 2³ = 8 2⁴ = 16 2⁵ = 32 2⁶ = 64 2⁷ = 128 2⁸ = 256 2⁹ = 512 2¹⁰ = 1024 2¹¹ = 2048 2¹² = 4096 Since 4096 is greater than 2304, we stop at 2¹¹ = 2048.

Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2¹¹ = 2048. 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, 2304. Since 2¹¹ is the number we are looking for, write 1 in the 2¹¹ place. Now the value of 2¹¹, which is 2048, is subtracted from 2304. 2304 - 2048 = 256.

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, 256. So, the next largest power of 2 is 2⁸, which is equal to 256. Now, we have to write 1 in the 2⁸ place. And then subtract 256 from 256. 256 - 256 = 0. We need to stop the process here since the remainder is 0.

Step 4 - Identify the unused place values: In step 2 and step 3, we wrote 1 in the 2¹¹ and 2⁸ places. Now, we can just write 0s in the remaining places. Now, by substituting the values, we get, 0 in the places 2⁰ to 2⁷ 1 in the 2⁸ place 0 in the places 2⁹ and 2¹⁰ 1 in the 2¹¹ place

Step 5 - Write the values in reverse order: We now write the numbers upside down to represent 2304 in binary. Therefore, 100100000000 is 2304 in binary.

Grouping Method: In this method, we divide the number 2304 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 2304 by 2. 2304 / 2 = 1152. Here, 1152 is the quotient and 0 is the remainder.

Step 2 - Divide the previous quotient (1152) by 2. 1152 / 2 = 576. Here, the quotient is 576 and the remainder is 0.

Step 3 - Repeat the previous step. 576 / 2 = 288. Now, the quotient is 288, and 0 is the remainder.

Step 4 - Repeat the previous step. 288 / 2 = 144. Now, the quotient is 144, and 0 is the remainder.

Step 5 - Repeat the previous step. 144 / 2 = 72. Now, the quotient is 72, and 0 is the remainder.

Step 6 - Repeat the previous step. 72 / 2 = 36. Now, the quotient is 36, and 0 is the remainder.

Step 7 - Repeat the previous step. 36 / 2 = 18. Now, the quotient is 18, and 0 is the remainder.

Step 8 - Repeat the previous step. 18 / 2 = 9. Now, the quotient is 9, and 0 is the remainder.

Step 9 - Repeat the previous step. 9 / 2 = 4. Now, the quotient is 4, and 1 is the remainder.

Step 10 - Repeat the previous step. 4 / 2 = 2. Now, the quotient is 2, and 0 is the remainder.

Step 11 - Repeat the previous step. 2 / 2 = 1. Now, the quotient is 1, and 0 is the remainder.

Step 12 - Repeat the previous step. 1 / 2 = 0. Here, the remainder is 1. And we stop the division here because the quotient is 0.

Step 13 - Write down the remainders from bottom to top. Therefore, 2304 (decimal) = 100100000000 (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 2304. Since the answer is 2¹¹, write 1 next to this power of 2. Subtract the value (2048) from 2304. So, 2304 - 2048 = 256. Find the largest power of 2 less than or equal to 256. The answer is 2⁸. So, write 1 next to this power. Now, 256 - 256 = 0. Since there is no remainder, we can write 0 next to the remaining powers. Final conversion will be 100100000000.

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, 2304 is divided by 2 to get 1152 as the quotient and 0 as the remainder. Now, 1152 is divided by 2. Here, we will get 576 as the quotient and 0 as the remainder. Dividing 576 by 2, we get 288 as the quotient and 0 as the remainder. Continue this process until the quotient becomes 0. Now, we write the remainders upside down to get the binary equivalent of 2304, 100100000000.

Rule 3: Representation Method

This rule also involves breaking the number into powers of 2. Identify the powers of 2 and write it down in decreasing order i.e., 2¹¹, 2¹⁰, 2⁹, etc. Find the largest power that fits into 2304. 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 2304, we use 0s for unused powers and 1s for 2¹¹ and 2⁸.

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 2304.

Memorize to speed up conversions: We can memorize the binary forms for numbers 1 to 16, and then use addition.

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, 2304 is even and its binary form is 100100000000. Here, the binary of 2304 ends in 0. If the number is odd, then its binary equivalent will end in 1. For example, the binary of 17 (an odd number) is 10001. 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 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 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 has occupied 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.

• Powers of 2: In binary, each place value corresponds to a power of 2. For example, 2⁰, 2¹, 2², etc.