Rivalry2

HTML Diff

0 added 0 removed

Original 2026-01-01

Modified 2026-02-28

1 3125 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 3125 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 2^11 = 2048 2^12 = 4096 Since 4096 is<a>greater than</a>3125, we stop at 2^11 = 2048.

4 Step 2 -Identify the largest power of 2: In the previous step, we stopped at 2^11 = 2048. 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, 3125. Since 2^11 is the number we are looking for, write 1 in the 2^11 place. Now the value of 2^11, which is 2048, is subtracted from 3125. 3125 - 2048 = 1077.

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, 1077. So, the next largest power of 2 is 2^10, which is less than or equal to 1077. Now, we have to write 1 in the 2^10 place. And then subtract 1024 from 1077. 1077 - 1024 = 53.

6 Step 4 -Continue the process: Continue identifying the largest power of 2 that fits into the remainder until the remainder is 0. For 53, the next largest power of 2 is 2^5. Write 1 in the 2^5 place and subtract 32 from 53. 53 - 32 = 21. Next, the largest power of 2 for 21 is 2^4. Write 1 in the 2^4 place and subtract 16 from 21. 21 - 16 = 5. For 5, the largest power of 2 is 2^2. Write 1 in the 2^2 place and subtract 4 from 5. 5 - 4 = 1. Finally, for 1, the largest power of 2 is 2^0. Write 1 in the 2^0 place and subtract 1 from 1. 1 - 1 = 0. We need to stop the process here since the remainder is 0.

7 Step 5 -Write the values: We now write the numbers in the correct order to represent 3125 in binary. Therefore, 110000110101 is 3125 in binary.

8 Grouping Method:In this method, we divide the number 3125 by 2. Let us see the step-by-step conversion.

9 Step 1 -Divide the given number 3125 by 2. 3125 / 2 = 1562. Here, 1562 is the quotient, and 1 is the remainder.

10 Step 2 -Divide the previous quotient (1562) by 2. 1562 / 2 = 781. Here, the quotient is 781 and the remainder is 0.

11 Step 3 -Repeat the previous step. 781 / 2 = 390. Now, the quotient is 390, and 1 is the remainder.

12 Step 4 -Continue this process until the quotient becomes 0. 390 / 2 = 195 remainder 0 195 / 2 = 97 remainder 1 97 / 2 = 48 remainder 1 48 / 2 = 24 remainder 0 24 / 2 = 12 remainder 0 12 / 2 = 6 remainder 0 6 / 2 = 3 remainder 0 3 / 2 = 1 remainder 1 1 / 2 = 0 remainder 1

13 Step 5 -Write down the remainders from bottom to top. Therefore, 3125 (decimal) = 110000110101 (binary).