1337 in Binary

The process of converting 1337 from decimal to binary involves dividing the number 1337 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 1337 to binary. In the last step, the remainder is noted down from bottom side up, and that becomes the converted value.

For example, the remainders noted down after dividing 1337 by 2 until getting 0 as the quotient is 10100111001. 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 10100111001.

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 10100111001 in binary is indeed 1337 in the decimal number system.

1337 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 1337 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 2048 is greater than 1337, we stop at 2¹⁰ = 1024.

Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2¹⁰ = 1024. 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, 1337. Since 2¹⁰ is the number we are looking for, write 1 in the 2¹⁰ place. Now the value of 2¹⁰, which is 1024, is subtracted from 1337. 1337 - 1024 = 313.

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, 313. So, the next largest power of 2 is 2⁸ = 256, which is less than or equal to 313. Write 1 in the 2⁸ place. Then subtract 256 from 313. 313 - 256 = 57.

Step 4 - Identify the next largest power of 2: The next largest power of 2 that fits into 57 is 2⁵ = 32. Write 1 in the 2⁵ place. Then subtract 32 from 57. 57 - 32 = 25.

Step 5 - Identify the next largest power of 2: The next largest power of 2 that fits into 25 is 2⁴ = 16. Write 1 in the 2⁴ place. Then subtract 16 from 25. 25 - 16 = 9.

Step 6 - Identify the next largest power of 2: The next largest power of 2 that fits into 9 is 2³ = 8. Write 1 in the 2³ place. Then subtract 8 from 9. 9 - 8 = 1.

Step 7 - Identify the next largest power of 2: The next largest power of 2 that fits into 1 is 2⁰ = 1. Write 1 in the 2⁰ place. Then subtract 1 from 1. 1 - 1 = 0.

Step 8 - Fill in the remaining places with 0: Insert 0 in the places that were not used (2⁹, 2⁷, 2⁶, 2², and 2¹). 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 1 in the 2⁴ place 1 in the 2³ place 0 in the 2² place 0 in the 2¹ place 1 in the 2⁰ place

Step 9 - Write the values in reverse order: We now write the numbers upside down to represent 1337 in binary. Therefore, 10100111001 is 1337 in binary.

Grouping Method: In this method, we divide the number 1337 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 1337 by 2. 1337 / 2 = 668. Here, 668 is the quotient, and 1 is the remainder.

Step 2 - Divide the previous quotient (668) by 2. 668 / 2 = 334. Here, the quotient is 334, and the remainder is 0.

Step 3 - Repeat the previous step. 334 / 2 = 167. Now, the quotient is 167, and 0 is the remainder.

Step 4 - Repeat the previous step. 167 / 2 = 83. Here, the remainder is 1.

Step 5 - Repeat the previous step. 83 / 2 = 41. Here, the remainder is 1.

Step 6 - Repeat the previous step. 41 / 2 = 20. Here, the remainder is 1.

Step 7 - Repeat the previous step. 20 / 2 = 10. Here, the remainder is 0.

Step 8 - Repeat the previous step. 10 / 2 = 5. Here, the remainder is 0.

Step 9 - Repeat the previous step. 5 / 2 = 2. Here, the remainder is 1.

Step 10 - Repeat the previous step. 2 / 2 = 1. Here, the remainder is 0.

Step 11 - Repeat the previous step. 1 / 2 = 0. Here, the remainder is 1. We stop the division here because the quotient is 0.

Step 12 - Write down the remainders from bottom to top. Therefore, 1337 (decimal) = 10100111001 (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 1337. Since the answer is 2¹⁰, write 1 next to this power of 2. Subtract the value (1024) from 1337. So, 1337 - 1024 = 313. Find the largest power of 2 less than or equal to 313. The answer is 2⁸. So, write 1 next to this power. Now, 313 - 256 = 57. Find the largest power of 2 less than or equal to 57. The answer is 2⁵. So, write 1 next to this power. Now, 57 - 32 = 25. Continue this process until the remainder is 0, writing 0s in unused places. Final conversion will be 10100111001.

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, 1337 is divided by 2 to get 668 as the quotient and 1 as the remainder. Now, 668 is divided by 2. Here, we will get 334 as the quotient and 0 as the remainder. Continue dividing until the quotient becomes 0, writing the remainders upside down to get the binary equivalent of 1337, 10100111001.

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, ..., 2⁰. Find the largest power that fits into 1337. 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 1337, use 1s for 2¹⁰, 2⁸, 2⁵, 2⁴, 2³, and 2⁰, and 0s for the 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 1337.

Memorize to speed up conversions: We can memorize the binary forms for numbers up to 1337.

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 Continue recognizing patterns for larger numbers.

Even and odd rule: Whenever a number is even, its binary form will end in 0. If the number is odd, then its binary equivalent will end in 1. For example, the binary of 1337 (an odd number) is 10100111001, ending 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 in 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.

• Grouping Method: A method of converting decimal numbers to binary by repeatedly dividing the number by 2 and recording the remainders.