2147483648 in Binary

The process of converting 2147483648 from decimal to binary involves dividing the number 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 2147483648 to binary. In the last step, the remainder is noted down from bottom to top, and that becomes the converted value. For example, the remainders noted down after dividing 2147483648 by 2 until getting 0 as the quotient is 10000000000000000000000000000000. Remember, the remainders here have been written upside down.

In the table shown below, the first column shows the binary digits (1 and 0) of 2147483648. 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 10000000000000000000000000000000 in binary is indeed 2147483648 in the decimal number system.

2147483648 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 2147483648 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 ... 2³¹ = 2147483648 Since 2³¹ equals 2147483648, we stop at this power.

Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2³¹ because it equals 2147483648. This is the exact number we are converting, so write 1 in the 2³¹ place. Since no subtraction is needed, all other places will be filled with 0s.

Step 3 - Identify the unused place values: Since we wrote 1 in the 2³¹ place, we can just write 0s in all the remaining places, from 2⁰ to 2³⁰. Now, by substituting the values, we get: 0 in the 2⁰ place 0 in the 2¹ place ... 0 in the 2³⁰ place 1 in the 2³¹ place

Step 4 - Write the values in reverse order: We now write the numbers upside down to represent 2147483648 in binary. Therefore, 10000000000000000000000000000000 is 2147483648 in binary.

Grouping Method: In this method, we divide the number 2147483648 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 2147483648 by 2. 2147483648 / 2 = 1073741824. Here, 1073741824 is the quotient and 0 is the remainder.

Step 2 - Continue dividing the quotient by 2 until the quotient becomes 0, noting down remainders at each step. This process will result in a series of 31 zeros followed by a 1 as the quotient becomes 0.

Step 3 - Write down the remainders from bottom to top. Therefore, 2147483648 (decimal) = 10000000000000000000000000000000 (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 2147483648. Since the answer is 2³¹, write 1 next to this power of 2. No subtraction is needed as 2³¹ equals 2147483648. Write 0 next to the remaining powers (2⁰ to 2³⁰). Final conversion will be 10000000000000000000000000000000.

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, 2147483648 is divided by 2 to get 1073741824 as the quotient and 0 as the remainder. Continue dividing the quotient by 2 until the quotient becomes 0. Write the remainders upside down to get the binary equivalent of 2147483648, 10000000000000000000000000000000.

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., from 2³¹ to 2⁰. Find the largest power that fits into 2147483648. 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 2147483648, we use 1 for 2³¹ and 0s for all other powers.

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 2147483648.

• Memorize powers of 2: Knowing the powers of 2 up to 2³¹ can help speed up conversions.
   
• Recognize the patterns: Notice the pattern when converting powers of 2 to binary. Each new power of 2 is simply 1 followed by zeros equal to the power.
   
• Even and odd rule: Whenever a number is even, its binary form will end in 0. 2147483648 is even, and its binary form ends in 0.
   
• Cross-verify the answers: Once the conversion is done, 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 the base 2 number system.

• Place value: Every digit has a value based on its position in a given number. For e.g., 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.

• Power of 2: Refers to numbers like 1, 2, 4, 8, etc., which are results of raising 2 to a power.