Rivalry2

HTML Diff

0 added 0 removed

Original 2026-01-01

Modified 2026-02-28

1 210 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 210 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. 20 = 1 21 = 2 22 = 4 23 = 8 24 = 16 25 = 32 26 = 64 27 = 128 28 = 256 Since 256 is<a>greater than</a>210, we stop at 27 = 128.

4 Step 2 -Identify the largest power of 2: In the previous step, we stopped at 27 = 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, 210. Since 27 is the number we are looking for, write 1 in the 27 place. Now the value of 27, which is 128, is subtracted from 210. 210 - 128 = 82.

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, 82. The next largest power of 2 is 26, which is less than or equal to 82. Now, we have to write 1 in the 26 place. And then subtract 64 from 82. 82 - 64 = 18.

6 Step 4 -Repeat the process: Next, find the largest power of 2 that fits into 18. The largest power is 24. Write 1 in the 24 place and subtract 16 from 18. 18 - 16 = 2.

7 Step 5 -Identify the last power of 2: Finally, for 2, write 1 in the 21 place and subtract 2. 2 - 2 = 0. We need to stop the process here since the remainder is 0.

8 Step 6 -Identify the unused place values: In the previous steps, we wrote 1 in the 27, 26, 24, and 21 places. Now, we can just write 0s in the remaining places, which are 25, 23, 22, and 20. Now, by substituting the values, we get: 0 in the 20 place 1 in the 21 place 0 in the 22 place 0 in the 23 place 1 in the 24 place 0 in the 25 place 1 in the 26 place 1 in the 27 place

9 Step 7 -Write the values in reverse order: We now write the numbers upside down to represent 210 in binary. Therefore, 11010010 is 210 in binary.

10 Grouping Method:In this method, we divide the number 210 by 2. Let us see the step-by-step conversion.

11 Step 1 -Divide the given number 210 by 2. 210 / 2 = 105. Here, 105 is the quotient and 0 is the remainder.

12 Step 2 -Divide the previous quotient (105) by 2. 105 / 2 = 52. Here, the quotient is 52 and the remainder is 1.

13 Step 3 -Repeat the previous step. 52 / 2 = 26. Now, the quotient is 26, and 0 is the remainder.

14 Step 4 -Repeat the previous step. 26 / 2 = 13. Here, the remainder is 0.

15 Step 5 -Continue the process. 13 / 2 = 6. Here, the quotient is 6 and the remainder is 1. 6 / 2 = 3. Here, the quotient is 3 and the remainder is 0. 3 / 2 = 1. Here, the quotient is 1 and the remainder is 1. 1 / 2 = 0. Here, the remainder is 1. And we stop the<a>division</a>here because the quotient is 0.

16 Step 6 -Write down the remainders from bottom to top. Therefore, 210 (decimal) = 11010010 (binary).