10000 in Binary
2026-02-28 01:03 Diff
https://brightchamps.com/en-us/math/numbers/10000-in-binary

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.

Expansion Method: Let us see the step-by-step process of converting 10000 using the expansion method.

Step 1 - Figure out the place values: In the binary system, each place value is a power 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
29 = 512
210 = 1024
211 = 2048
212 = 4096
213 = 8192
214 = 16384

Since 16384 is greater than 10000, we stop at 213 = 8192.

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 less than 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.

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.

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.

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.

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

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

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

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

Step 4 - Continue dividing until the quotient becomes 0.

1250 / 2 = 625. Remainder 0.

625 / 2 = 312. Remainder 1.

312 / 2 = 156. Remainder 0.

156 / 2 = 78. Remainder 0.

78 / 2 = 39. Remainder 0.

39 / 2 = 19. Remainder 1.

19 / 2 = 9. Remainder 1.

9 / 2 = 4. Remainder 1.

4 / 2 = 2. Remainder 0.

2 / 2 = 1. Remainder 0.

1 / 2 = 0. Remainder 1.

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