Rivalry2

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Original 2026-01-01

Modified 2026-02-28

1 215 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 215 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

8 24 = 16

9 25 = 32

10 26 = 64

11 27 = 128

12 28 = 256

13 Since 256 is<a>greater than</a>215, we stop at 27 = 128.

14 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, 215. 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 215. 215 - 128 = 87.

15 Step 3- Identify the next largest power of 2:

16 In this step, we need to find the largest power of 2 that fits into the result of the previous step, 87. So, the next largest power of 2 is 26, which is less than or equal to 87. Now, we have to write 1 in the 26 places. And then subtract 64 from 87. 87 - 64 = 23.

17 Step 4- Repeat the process for the remaining value: Continue finding the largest suitable power of 2 for the remainder 23, which is 24 = 16. Write 1 in the 24 place and subtract 16 from 23.

18 23 - 16 = 7.

19 For 7, the largest power of 2 is 22 = 4.

20 Write 1 in the 22 place and subtract 4 from 7.

21 7 - 4 = 3. Finally, for 3, the largest power of 2 is 21 = 2.

22 Write 1 in the 21 place and subtract 2 from 3.

23 3 - 2 = 1.

24 Finally, 1 is 20.

25 Step 5- Identify the unused place values:

26 In step 2 to 4, we wrote 1 in the 27, 26, 24, 22, 21, and 20 places.

27 Now, we can just write 0s in the remaining places, which are 25 and 23.

28 Now, by substituting the values, we get, 1 in the 27 place 1 in the 26 place 0 in the 25 place 1 in the 24 place 0 in the 23 place 1 in the 22 place 1 in the 21 place 1 in the 20 place

29 Step 6- Write the values in reverse order: We now write the numbers upside down to represent 215 in binary.

30 Therefore, 11010111 is 215 in binary.

31 Grouping Method: In this method, we divide the number 215 by 2. Let us see the step-by-step conversion.

32 Step 1- Divide the given number 215 by 2. 215 / 2 = 107. Here, 107 is the quotient and 1 is the remainder.

33 Step 2- Divide the previous quotient (107) by 2. 107 / 2 = 53. Here, the quotient is 53 and the remainder is 1.

34 Step 3- Repeat the previous step. 53 / 2 = 26. Now, the quotient is 26, and 1 is the remainder.

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

36 Step 5- Repeat the previous step. 13 / 2 = 6. Here, the remainder is 1.

37 Step 6- Repeat the previous step. 6 / 2 = 3. Here, the remainder is 0.

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

39 Step 8- Repeat the previous step. 1 / 2 = 0. Here, the remainder is 1. And we stop the<a>division</a>here because the quotient is 0.

40 Step 9- Write down the remainders from bottom to top.

41 Therefore, 215 (decimal) = 11010111 (binary).