Rivalry2

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Original 2026-01-01

Modified 2026-02-28

1 225 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.

2 Expansion Method:Let us see the step-by-step process of converting 225 using the expansion method.

3 Step 1 -Figure out the place values: In the binary system, each<a>place value</a>is a<a>power</a>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<a>2^5</a>= 32 2^6 = 64 2^7 = 128 2^8 = 256 Since 256 is<a>greater than</a>225, we stop at 2^7 = 128.

4 Step 2 -Identify the largest power of 2: In the previous step, we stopped at 2^7 = 128. This is because in this step, we have to identify the largest power of 2, which is<a>less than</a>or equal to the given number, 225. Since 2^7 is the number we are looking for, write 1 in the 2^7 place. Now the value of 2^7, which is 128, is subtracted from 225. 225 - 128 = 97.

5 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, 97. So, the next largest power of 2 is 2^6, which is 64. Now, we have to write 1 in the 2^6 place. And then subtract 64 from 97. 97 - 64 = 33.

6 Step 4 -Continue the process: Find the next largest power of 2 that fits into 33, which is 2^5 = 32. Write 1 in the 2^5 place. 33 - 32 = 1.

7 Step 5 -Find the next largest power of 2 for 1, which is 2^0 = 1. Write 1 in the 2^0 place. 1 - 1 = 0. We need to stop the process here since the remainder is 0.

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

9 Step 7 -Write the values in reverse order: We now write the numbers upside down to represent 225 in binary. Therefore, 11100001 is 225 in binary.

10 Grouping Method:In this method, we divide the number 225 by 2. Let us see the step-by-step conversion.

11 Step 1 -Divide the given number 225 by 2. 225 / 2 = 112. Here, 112 is the quotient and 1 is the remainder.

12 Step 2 -Divide the previous quotient (112) by 2. 112 / 2 = 56. Here, the quotient is 56 and the remainder is 0.

13 Step 3 -Repeat the previous step. 56 / 2 = 28. Now, the quotient is 28, and 0 is the remainder.

14 Step 4 -Repeat the previous step. 28 / 2 = 14. Here, the quotient is 14, and 0 is the remainder.

15 Step 5 -Repeat the previous step. 14 / 2 = 7. Here, the quotient is 7, and 0 is the remainder.

16 Step 6 -Repeat the previous step. 7 / 2 = 3. Here, the quotient is 3, and 1 is the remainder.

17 Step 7 -Repeat the previous step. 3 / 2 = 1. Here, the quotient is 1, and 1 is the remainder.

18 Step 8 -Repeat the previous step. 1 / 2 = 0.

19 Here, the remainder is 1. And we stop the<a>division</a>here because the quotient is 0.

20 Step 9 -Write down the remainders from bottom to top. Therefore, 225 (decimal) = 11100001 (binary).