364 in Binary

The process of converting 364 from decimal to binary involves dividing the number 364 by 2. Here, 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 364 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 364 by 2 until getting 0 as the quotient is 101101100. 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 101101100.

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 101101100 in binary is indeed 364 in the decimal number system.

364 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 364 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

Since 256 is less than 364, we start with 2⁸ = 256.

Step 2 - Identify the largest power of 2: In the previous step, we started at 2^8 = 256. 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, 364. Since 2⁸ is the number we are looking for, write 1 in the 2⁸ place. Now, the value of 2⁸, which is 256, is subtracted from 364. 364 - 256 = 108.

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, 108. So, the next largest power of 2 is 2⁶, which is less than or equal to 108. Now, we have to write 1 in the 2⁶ place. And then subtract 64 from 108. 108 - 64 = 44.

Step 4 - Continue the process: Repeat the previous steps until the remainder is 0. 44 - 32 = 12 (write 1 in the 2^5 place) 12 - 8 = 4 (write 1 in the 2³ place) 4 - 4 = 0 (write 1 in the 2² place)

Step 5 - Identify the unused place values: In the steps above, we've written 1s in the 2⁸, 2⁶, 2⁵, 2³, and 2² places. Now, we can just write 0s in the remaining places, which are 2⁷, 2⁴, 2¹, and 2⁰. Now, by substituting the values, we get: 0 in the 2⁷ place 0 in the 2⁴ place 0 in the 2¹ place 0 in the 2⁰ place Therefore, 101101100 is 364 in binary.

Grouping Method: In this method, we divide the number 364 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 364 by 2. 364 / 2 = 182. Here, 182 is the quotient and 0 is the remainder.

Step 2 - Divide the previous quotient (182) by 2. 182 / 2 = 91. Here, the quotient is 91 and the remainder is 0.

Step 3 - Repeat the previous step. 91 / 2 = 45. Now, the quotient is 45, and 1 is the remainder.

Step 4 - Repeat the previous step. 45 / 2 = 22. Here, the quotient is 22, and 1 is the remainder. Continue this process until you reach a quotient of 0. 22 / 2 = 11, remainder 0 11 / 2 = 5, remainder 1 5 / 2 = 2, remainder 1 2 / 2 = 1, remainder 0 1 / 2 = 0, remainder 1

Step 5 - Write down the remainders from bottom to top. Therefore, 364 (decimal) = 101101100 (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 364. Since the answer is 2⁸, write 1 next to this power of 2. Subtract the value (256) from 364. So, 364 - 256 = 108. Find the largest power of 2 less than or equal to 108. The answer is 2⁶. So, write 1 next to this power. Now, 108 - 64 = 44. Continue this process until the remainder is 0. Final conversion will be 101101100.

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, 364 is divided by 2 to get 182 as the quotient and 0 as the remainder. Now, 182 is divided by 2. Here, we will get 91 as the quotient and 0 as the remainder. Dividing 91 by 2, we get 1 as the remainder and 45 as the quotient. Continue this process until you reach a quotient of 0. Now, we write the remainders upside down to get the binary equivalent of 364, 101101100.

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., 2⁸, 2⁷, 2⁶, 2⁵, 2⁴, 2³, 2², 2¹, and 2⁰. Find the largest power that fits into 364. 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. For 364, we use 1s for 2⁸, 2⁶, 2⁵, 2³, and 2², and 0s for 2⁷, 2⁴, 2¹, and 2⁰.

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 364.

Memorize to speed up conversions: We can memorize the binary forms for numbers like 1 to 16, as they are commonly used.

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, 364 is even and its binary form is 101101100. Here, the binary of 364 ends in 0. 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 the base 2 number system.

• Place value: Every digit has a value based on its position in a given number. For example, in 364 (base 10), 3 has occupied the hundreds place, 6 is in the tens place, and 4 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 can be expressed as 2 raised to an integer power, such as 2⁰, 2¹, 2², etc.