364 in Binary
2026-02-28 21:35 Diff
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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).