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Original 2026-01-01

Modified 2026-02-28

1 10000 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 10000 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 21 = 2 22 = 4 23 = 8 24 = 16 25 = 32 26 = 64 27 = 128 28 = 256 29 = 512 210 = 1024 211 = 2048 212 = 4096 213 = 8192 214 = 16384

5 Since 16384 is<a>greater than</a>10000, we stop at 213 = 8192.

6 Step 2- Identify the largest power of 2: In the previous step, we stopped at 213 = 8192. 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, 10000. Since 213 is the number we are looking for, write 1 in the 213 place. Now the value of 213, which is 8192, is subtracted from 10000. 10000 - 8192 = 1808.

7 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, 1808. So, the next largest power of 2 is 210, which is less than or equal to 1808. Now, we have to write 1 in the 210 place. And then subtract 1024 from 1808. 1808 - 1024 = 784.

8 Step 4- Continue the process: Repeat the steps by finding the next largest powers of 2 that fit into the remaining number, and write 1s in those places, subtracting each time. Fill in 0s for unused place values. Now, by substituting the values, we get, 1 in the 213 place 0 in the 212 place 0 in the 211 place 1 in the 210 place 1 in the 29 place 1 in the 28 place 0 in the 27 place 0 in the 26 place 0 in the 25 place 1 in the 24 place 0 in the 23 place 0 in the 22 place 0 in the 21 place 0 in the 20 place.

9 Step 5- Write the values in reverse order: We now write the numbers upside down to represent 10000 in binary. Therefore, 10011100010000 is 10000 in binary.

10 Grouping Method: In this method, we divide the number 10000 by 2. Let us see the step-by-step conversion.

11 Step 1- Divide the given number 10000 by 2. 10000 / 2 = 5000. Here, 5000 is the quotient and 0 is the remainder.

12 Step 2- Divide the previous quotient (5000) by 2. 5000 / 2 = 2500. Here, the quotient is 2500 and the remainder is 0.

13 Step 3- Repeat the previous step. 2500 / 2 = 1250. Now, the quotient is 1250, and 0 is the remainder.

14 Step 4- Continue dividing until the quotient becomes 0.

15 1250 / 2 = 625. Remainder 0.

16 625 / 2 = 312. Remainder 1.

17 312 / 2 = 156. Remainder 0.

18 156 / 2 = 78. Remainder 0.

19 78 / 2 = 39. Remainder 0.

20 39 / 2 = 19. Remainder 1.

21 19 / 2 = 9. Remainder 1.

22 9 / 2 = 4. Remainder 1.

23 4 / 2 = 2. Remainder 0.

24 2 / 2 = 1. Remainder 0.

25 1 / 2 = 0. Remainder 1.

26 Step 5- Write down the remainders from bottom to top. Therefore, 10000 (decimal) = 10011100010000 (binary).