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Original 2026-01-01

Modified 2026-02-28

1 1085 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 1085 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<a>less than</a>1085, we stop at 2^10 = 1024.

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 less than or equal to the given number, 1085. Since 2^10 is the number we are looking for, write 1 in the 2^10 place. Now the value of 2^10, which is 1024, is subtracted from 1085. 1085 - 1024 = 61.

5 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, 61. So, the next largest power of 2 is 2^5 = 32. Now, we have to write 1 in the 2^5 place. And then subtract 32 from 61. 61 - 32 = 29.

6 Step 4 -Continue with the remaining value: The next largest power of 2 for 29 is 2^4 = 16. Write 1 in the 2^4 place. Now subtract 16 from 29. 29 - 16 = 13.

7 Step 5 -Continue until the remainder is zero: The next largest power of 2 for 13 is 2^3 = 8. Write 1 in the 2^3 place. Now subtract 8 from 13. 13 - 8 = 5. The next largest power of 2 for 5 is 2^2 = 4. Write 1 in the 2^2 place. Now subtract 4 from 5. 5 - 4 = 1. The next largest power of 2 for 1 is 2^0 = 1. Write 1 in the 2^0 place. Now subtract 1 from 1. 1 - 1 = 0.

8 Step 6 -Fill remaining places with zeros: We can just write 0s in the remaining places, which are 2^9, 2^8, 2^7, 2^6, and 2^1. Now, by substituting the values, we get, 0 in the 2^9 place 0 in the 2^8 place 0 in the 2^7 place 0 in the 2^6 place 1 in the 2^5 place 1 in the 2^4 place 1 in the 2^3 place 1 in the 2^2 place 0 in the 2^1 place 1 in the 2^0 place Therefore, 10000111101 is 1085 in binary.

9 Grouping Method:In this method, we divide the number 1085 by 2. Let us see the step-by-step conversion.

10 Step 1 -Divide the given number 1085 by 2. 1085 / 2 = 542. Here, 542 is the quotient and 1 is the remainder.

11 Step 2 -Divide the previous quotient (542) by 2. 542 / 2 = 271. Here, the quotient is 271 and the remainder is 0.

12 Step 3 -Repeat the previous step. 271 / 2 = 135. Now, the quotient is 135 and the remainder is 1.

13 Step 4 -Repeat the previous step. 135 / 2 = 67. Here, the remainder is 1.

14 Step 5 -Repeat the previous step. 67 / 2 = 33. Here, the remainder is 1.

15 Step 6 -Repeat the previous step. 33 / 2 = 16. Here, the remainder is 1.

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

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

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

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

20 Step 11 -Repeat the previous step. 1 / 2 = 0. Here, the remainder is 1.

21 Step 12 -Write down the remainders from bottom to top. Therefore, 1085 (decimal) = 10000111101 (binary).