1313 in Binary

The process of converting 1313 from decimal to binary involves dividing the number 1313 by 2. It is 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 1313 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 1313 by 2 until getting 0 as the quotient result in 10100100001. 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 10100100001.

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 10100100001 in binary is indeed 1313 in the decimal number system.

1313 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 1313 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 Since 1024 is the largest power less than 1313, we use it to start.

Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2¹⁰ = 1024. This is because we have to identify the largest power of 2, which is less than or equal to the given number, 1313. Since 2¹⁰ is the number we are looking for, write 1 in the 2¹⁰ place. Now subtract the value of 2¹⁰, which is 1024, from 1313. 1313 - 1024 = 289.

Step 3 - Identify the next largest power of 2: In this step, we need to find the largest power of 2 that fits into 289. The next largest power of 2 is 2⁸, which is 256. Write 1 in the 2⁸ place. Subtract 256 from 289. 289 - 256 = 33.

Step 4 - Repeat the process: Continue finding the next largest powers of 2 that fit into the remainder, 33. The powers are 2⁵ = 32 and 2⁰ = 1. Write 1 in the 2⁵ and 2⁰ places. Subtract the corresponding values from the remainder. 33 - 32 = 1. 1 - 1 = 0.

Step 5 - Fill in the remaining powers: Write 0s in the places that were not used, which are 2⁹, 2⁷, 2⁶, 2⁴, 2³, 2², and 2¹. Now, by substituting the values, we get: 0 in the 2⁹ place 1 in the 2⁸ place 0 in the 2⁷ place 0 in the 2⁶ place 1 in the 2⁵ place 0 in the 2⁴ place 0 in the 2³ place 0 in the 2² place 0 in the 2¹ place 1 in the 2⁰ place

Step 6 - Write the values in sequence: The binary representation of 1313 is 10100100001.

Grouping Method: In this method, we divide the number 1313 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 1313 by 2. 1313 / 2 = 656 with a remainder of 1.

Step 2 - Divide the previous quotient (656) by 2. 656 / 2 = 328 with a remainder of 0.

Step 3 - Repeat the previous step. 328 / 2 = 164 with a remainder of 0.

Step 4 - Repeat the previous step. 164 / 2 = 82 with a remainder of 0.

Step 5 - Continue the process until the quotient becomes 0. 82 / 2 = 41 with a remainder of 0. 41 / 2 = 20 with a remainder of 1. 20 / 2 = 10 with a remainder of 0. 10 / 2 = 5 with a remainder of 0. 5 / 2 = 2 with a remainder of 1. 2 / 2 = 1 with a remainder of 0. 1 / 2 = 0 with a remainder of 1.

Step 6 - Write down the remainders from bottom to top. The binary equivalent of 1313 is 10100100001.

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 1313. Since the answer is 2¹⁰, write 1 next to this power of 2. Subtract the value (1024) from 1313. So, 1313 - 1024 = 289. Find the largest power of 2 less than or equal to 289. The answer is 2⁸. So, write 1 next to this power. Now, continue this process with the remainders until you reach 0. Final conversion will be 10100100001.

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, 1313 is divided by 2 to get 656 as the quotient and 1 as the remainder. Now, 656 is divided by 2. Here, we will get 328 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 1313, which is 10100100001.

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., 2¹⁰, 2⁹, 2⁸, etc. Find the largest power that fits into 1313. 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 1313, we use 0s for the unused powers of 2.

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 1313.

Memorize to speed up conversions: We can memorize the binary forms for numbers like 1 to 20 and beyond.

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 instance, 1312 is even, and its binary form ends in 0. If the number is odd, then its binary equivalent will end in 1. For instance, the binary of 1313 ends 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 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.

• Power of 2: Refers to numbers that are powers of 2, such as 1, 2, 4, 8, 16, and so on. They are essential in understanding binary conversion.