Rivalry2

HTML Diff

0 added 0 removed

Original 2026-01-01

Modified 2026-02-28

1 2025 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 2025 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.

4 20 = 1

5 21 = 2

6 22 = 4

7 23 = 8 ... 210 = 1024 211 = 2048

8 Since 2048 is<a>greater than</a>2025, we stop at 210 = 1024.

9 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<a>less than</a>or equal to the given number, 2025. 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 2025. 2025 - 1024 = 1001.

10 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, 1001. So, the next largest power of 2 is 29 = 512. Now, we have to write 1 in the 29 place. And then subtract 512 from 1001. 1001 - 512 = 489.

11 Step 4- Continue the process: Repeat this process to find the next powers of 2 that fit into the result and subtract until you reach 0, writing 1s and 0s as needed. 489 - 256 = 233 (28 = 256) 233 - 128 = 105 (27 = 128) 105 - 64 = 41 (26 = 64) 41 - 32 = 9 (25 = 32) 9 - 8 = 1 (23 = 8) 1 - 1 = 0 (20 = 1) Now, by substituting the values, we get, 1 in the 210 place 1 in the 29 place 1 in the 28 place 1 in the 27 place 1 in the 2^6 place 1 in the 25 place 0 in the 24 place 0 in the 23 place 1 in the 22 place 0 in the 21 place 1 in the 20 place

12 Step 5- Write the values in reverse order: We now write the numbers upside down to represent 2025 in binary. Therefore, 11111100101 is 2025 in binary.

13 Grouping Method: In this method, we divide the number 2025 by 2. Let us see the step-by-step conversion.

14 Step 1- Divide the given number 2025 by 2. 2025 / 2 = 1012. Here, 1012 is the quotient and 1 is the remainder.

15 Step 2- Divide the previous quotient (1012) by 2. 1012 / 2 = 506. Here, the quotient is 506 and the remainder is 0.

16 Step 3- Repeat the previous step. 506 / 2 = 253. Now, the quotient is 253, and 0 is the remainder.

17 Step 4- Repeat the previous step. 253 / 2 = 126. Here, the remainder is 1. Continue this process until the quotient becomes 0. Finally, write down the remainders from bottom to top. Therefore, 2025 (decimal) = 11111100101 (binary).