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Original 2026-01-01

Modified 2026-02-28

1 2000 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 2000 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 ...

9 210 = 1024

10 211 = 2048

11 Since 2048 is<a>greater than</a>2000, we stop at 210 = 1024.

12 Step 2- Identify the largest power of 2:

13 In the previous step, we stopped at 210 = 1024.

14 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, 2000.

15 Since 210 is the number we are looking for, write 1 in the 210 place.

16 Now the value of 210, which is 1024, is subtracted from 2000. 2000 - 1024 = 976.

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

18 In this step, we need to find the largest power of 2 that fits into the result of the previous step, 976.

19 The next largest power of 2 is 2^9, which is 512. Now, we write 1 in the 29 place.

20 And then subtract 512 from 976. 976 - 512 = 464.

21 Step 4- Continue identifying the largest power of 2: The next power is 28 = 256, which fits into 464. 464 - 256 = 208.

22 Step 5- Continue the process: The next power is 27 = 128. 208 - 128 = 80.

23 Step 6- Continue the process: The next power is 26 = 64. 80 - 64 = 16.

24 Step 7- Continue the process: The next power is 24 = 16. 16 - 16 = 0.

25 Step 8- Identify the unused place values: In the steps above, we wrote 1 in the 210, 29, 28, 27, 26, and 24 places.

26 Now, we can just write 0s in the remaining places.

27 Now, by substituting the values, we get, 0 in the 20 place 0 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 1 in the 28 place 1 in the 29 place 1 in the 210 place

28 Step 9- Write the values in reverse order: We now write the numbers upside down to represent 2000 in binary. Therefore, 11111010000 is 2000 in binary.

29 Grouping Method: In this method, we divide the number 2000 by 2. Let us see the step-by-step conversion.

30 Step 1- Divide the given number 2000 by 2. 2000 / 2 = 1000. Here, 1000 is the quotient and 0 is the remainder.

31 Step 2- Divide the previous quotient (1000) by 2. 1000 / 2 = 500. Here, the quotient is 500 and the remainder is 0.

32 Step 3- Repeat the previous step. 500 / 2 = 250. Now, the quotient is 250, and 0 is the remainder.

33 Step 4- Repeat the previous step. 250 / 2 = 125. Now, the quotient is 125, and 0 is the remainder.

34 Step 5- Repeat the previous step. 125 / 2 = 62. Now, the quotient is 62, and 1 is the remainder.

35 Step 6- Repeat the previous step. 62 / 2 = 31. Now, the quotient is 31, and 0 is the remainder.

36 Step 7- Repeat the previous step. 31 / 2 = 15. Now, the quotient is 15, and 1 is the remainder.

37 Step 8- Repeat the previous step. 15 / 2 = 7. Now, the quotient is 7, and 1 is the remainder.

38 Step 9- Repeat the previous step. 7 / 2 = 3. Now, the quotient is 3, and 1 is the remainder.

39 Step 10- Repeat the previous step. 3 / 2 = 1. Now, the quotient is 1, and 1 is the remainder.

40 Step 11- 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.

41 Step 12- Write down the remainders from bottom to top.

42 Therefore, 2000 (decimal) = 11111010000 (binary).