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Original 2026-01-01

Modified 2026-02-28

1 1024 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 1024 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 2^9 = 512 2^10 = 1024 Since 1024 is equal to 2^10, we stop at 2^10.

4 Step 2 -Identify the largest power of 2: In the previous step, we stopped at 2^10 = 1024. This is because in this step, we have to identify the largest power of 2, which is equal to the given number, 1024. Since 2^10 is the number we are looking for, write 1 in the 2^10 place. Now the value of 1024 is achieved, and we have no remainder.

5 Step 3 -Identify the unused place values: Since we have used 2^10, we can just write 0s in all the remaining places, which are 2^0 to 2^9. Now, by substituting the values, we get, 0 in the 2^0 place 0 in the 2^1 place 0 in the 2^2 place 0 in the 2^3 place 0 in the 2^4 place 0 in the 2^5 place 0 in the 2^6 place 0 in the 2^7 place 0 in the 2^8 place 0 in the 2^9 place 1 in the 2^10 place

6 Step 4 -Write the values in reverse order: We now write the numbers upside down to represent 1024 in binary. Therefore, 10000000000 is 1024 in binary.

7 Grouping Method:In this method, we divide the number 1024 by 2. Let us see the step-by-step conversion.

8 Step 1 - Divide the given number 1024 by 2. 1024 / 2 = 512. Here, 512 is the quotient and 0 is the remainder.

9 Step 2 - Divide the previous quotient (512) by 2. 512 / 2 = 256. Here, the quotient is 256 and the remainder is 0.

10 Step 3 - Repeat the previous step. 256 / 2 = 128. Now, the quotient is 128, and 0 is the remainder.

11 Step 4 - Repeat the previous step. 128 / 2 = 64. Here, the quotient is 64 and the remainder is 0.

12 Step 5 - Repeat the previous step. 64 / 2 = 32. Here, the quotient is 32 and the remainder is 0.

13 Step 6 - Repeat the previous step. 32 / 2 = 16. Here, the quotient is 16 and the remainder is 0.

14 Step 7 - Repeat the previous step. 16 / 2 = 8. Here, the quotient is 8 and the remainder is 0.

15 Step 8 - Repeat the previous step. 8 / 2 = 4. Here, the quotient is 4 and the remainder is 0.

16 Step 9 - Repeat the previous step. 4 / 2 = 2. Here, the quotient is 2 and the remainder is 0.

17 Step 10 - Repeat the previous step. 2 / 2 = 1. Here, the quotient is 1 and the remainder is 0.

18 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.

19 Step 12 - Write down the remainders from bottom to top. Therefore, 1024 (decimal) = 10000000000 (binary).