617 in Binary

The process of converting 617 from decimal to binary involves dividing the number 617 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 617 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 617 by 2 until getting 0 as the quotient is 1001101001. 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 1001101001.

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 1001101001 in binary is indeed 617 in the decimal number system.

617 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 617 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. 2^0 = 1 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 2^8 = 256 2^9 = 512 Since 512 is less than 617, we stop at 2^9 = 512.

Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2^9 = 512. 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, 617. Since 2^9 is the number we are looking for, write 1 in the 2^9 place. Now the value of 2^9, which is 512, is subtracted from 617. 617 - 512 = 105.

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, 105. The next largest power of 2 is 2^6, which is less than or equal to 105. Now, we have to write 1 in the 2^6 place. And then subtract 64 from 105. 105 - 64 = 41.

Step 4 - Repeat the process: Continue to find the next largest power of 2 for the result, 41. The largest power of 2 for 41 is 2^5 = 32. 41 - 32 = 9. Find the largest power of 2 for 9, which is 2^3 = 8. 9 - 8 = 1. Find the largest power of 2 for 1, which is 2^0 = 1. 1 - 1 = 0. We need to stop the process here since the remainder is 0.

Step 5 - Identify the unused place values: In previous steps, we wrote 1 in the 2^9, 2^6, 2^5, 2^3, and 2^0 places. Now, we can just write 0s in the remaining places, which are 2^8, 2^7, 2^4, 2^2, and 2^1. Now, by substituting the values, we get, 1 in the 2^9 place 0 in the 2^8 place 0 in the 2^7 place 1 in the 2^6 place 1 in the 2^5 place 0 in the 2^4 place 1 in the 2^3 place 0 in the 2^2 place 0 in the 2^1 place 1 in the 2^0 place Therefore, 1001101001 is 617 in binary.

Grouping Method: In this method, we divide the number 617 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 617 by 2. 617 / 2 = 308. Here, 308 is the quotient and 1 is the remainder.

Step 2 - Divide the previous quotient (308) by 2. 308 / 2 = 154. Here, the quotient is 154 and the remainder is 0.

Step 3 - Repeat the previous step. 154 / 2 = 77. Now, the quotient is 77, and 0 is the remainder.

Step 4 - Repeat the previous step. 77 / 2 = 38. Here, the remainder is 1.

Step 5 - Continue this process until the quotient becomes 0. 38 / 2 = 19, remainder 0. 19 / 2 = 9, remainder 1. 9 / 2 = 4, remainder 1. 4 / 2 = 2, remainder 0. 2 / 2 = 1, remainder 0. 1 / 2 = 0, remainder 1.

Step 6 - Write down the remainders from bottom to top. Therefore, 617 (decimal) = 1001101001 (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 617. Since the answer is 2^9, write 1 next to this power of 2. Subtract the value (512) from 617. So, 617 - 512 = 105. Find the largest power of 2 less than or equal to 105. The answer is 2^6. So, write 1 next to this power. Continue this process until the remainder is 0. Final conversion will be 1001101001.

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, 617 is divided by 2 to get 308 as the quotient and 1 as the remainder. Now, 308 is divided by 2. Here, we will get 154 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 617, 1001101001.

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., 2^9, 2^8, 2^7, and so on. Find the largest power that fits into 617. 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 617, we use a combination of 1s and 0s to represent its binary form.

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 617.

Memorize to speed up conversions: We can memorize the binary forms for numbers 1 to 15 as a starting point to speed up conversions.

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, 617 is odd, so its binary form, 1001101001, ends in 1. If the number is even, then its binary equivalent will end in 0.

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.

• Quotient: It is the result obtained when one number is divided by another.