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Original 2026-01-01

Modified 2026-02-28

1 4782 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 4782 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 ... 2^12 = 4096 2^13 = 8192 Since 8192 is<a>greater than</a>4782, we stop at 2^12 = 4096.

4 Step 2 -Identify the largest power of 2: In the previous step, we stopped at 2^12 = 4096. 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, 4782. Since 2^12 is the number we are looking for, write 1 in the 2^12 place. Now the value of 2^12, which is 4096, is subtracted from 4782. 4782 - 4096 = 686.

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, 686. So, the next largest power of 2 is 2^9, which is 512. Now, we have to write 1 in the 2^9 places. And then subtract 512 from 686. 686 - 512 = 174.

6 Step 4 -Continue identifying powers of 2: Repeat the process with 174, which is the result from the previous step. The largest power of 2 less than or equal to 174 is 2^7 = 128. Write 1 in the 2^7 place. Subtract 128 from 174: 174 - 128 = 46. Continue with 46. The largest power of 2 is<a>2^5</a>= 32. Write 1 in the 2^5 place. Subtract 32 from 46: 46 - 32 = 14. Finally, for 14, the largest power of 2 is 2^3 = 8. Write 1 in the 2^3 place. Subtract 8 from 14: 14 - 8 = 6. For 6, the largest power of 2 is 2^2 = 4. Write 1 in the 2^2 place. Subtract 4 from 6: 6 - 4 = 2. For 2, the largest power of 2 is 2^1 = 2. Write 1 in the 2^1 place. Subtract 2 from 2: 2 - 2 = 0. We need to stop the process here since the remainder is 0.

7 Step 5 -Write the unused place values: In steps 2 to 4, we wrote 1 in the 2^12, 2^9, 2^7, 2^5, 2^3, 2^2, and 2^1 places. Now, we can just write 0s in the remaining places. 0 in the 2^11 place 0 in the 2^10 place 0 in the 2^8 place 0 in the 2^6 place 0 in the 2^4 place 0 in the 2^0 place

8 Step 6 -Write the values in reverse order: We now write the numbers upside down to represent 4782 in binary. Therefore, 1001010111110 is 4782 in binary.

9 Grouping Method:In this method, we divide the number 4782 by 2. Let us see the step-by-step conversion.

10 Step 1 -Divide the given number 4782 by 2. 4782 / 2 = 2391. Here, 2391 is the quotient and 0 is the remainder.

11 Step 2 -Divide the previous quotient (2391) by 2. 2391 / 2 = 1195. Here, the quotient is 1195 and the remainder is 1.

12 Step 3 -Repeat the previous step. 1195 / 2 = 597. Now, the quotient is 597 and 1 is the remainder.

13 Step 4 -Repeat the previous step. 597 / 2 = 298. The quotient is 298, and 1 is the remainder.

14 Step 5 -Repeat the previous step. 298 / 2 = 149. The quotient is 149, and 0 is the remainder.

15 Step 6 -Repeat the previous step. 149 / 2 = 74. The quotient is 74, and 1 is the remainder.

16 Step 7 -Repeat the previous step. 74 / 2 = 37. The quotient is 37, and 0 is the remainder.

17 Step 8 -Repeat the previous step. 37 / 2 = 18. The quotient is 18, and 1 is the remainder.

18 Step 9 -Repeat the previous step. 18 / 2 = 9. The quotient is 9, and 0 is the remainder.

19 Step 10 -Repeat the previous step. 9 / 2 = 4. The quotient is 4, and 1 is the remainder.

20 Step 11 -Repeat the previous step. 4 / 2 = 2. The quotient is 2, and 0 is the remainder.

21 Step 12 -Repeat the previous step. 2 / 2 = 1. The quotient is 1, and 0 is the remainder.

22 Step 13 -Repeat the previous step. 1 / 2 = 0. The quotient is 0, and 1 is the remainder. We stop the<a>division</a>here because the quotient is 0.

23 Step 14 -Write down the remainders from bottom to top. Therefore, 4782 (decimal) = 1001010111110 (binary).