Rivalry2

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Original 2026-01-01

Modified 2026-02-28

1 126 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 126 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 Since 128 is<a>greater than</a>126, we stop at 2^6 = 64.

4 Step 2 -Identify the largest power of 2: In the previous step, we stopped at 2^6 = 64. 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, 126. Since 2^6 is the number we are looking for, write 1 in the 2^6 place. Now the value of 2^6, which is 64, is subtracted from 126. 126 - 64 = 62.

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, 62. So, the next largest power of 2 is 2^5, which is 32. Now, we have to write 1 in the 2^5 place. And then subtract 32 from 62. 62 - 32 = 30.

6 Step 4 -Continue the process: Identify the next largest power of 2 that fits into the result of the previous step, 30. The next largest power of 2 is 2^4, which is 16. Write 1 in the 2^4 place. Subtract 16 from 30. 30 - 16 = 14.

7 Step 5 -Continue the process: Identify the next largest power of 2 that fits into the result of the previous step, 14. The next largest power of 2 is 2^3, which is 8. Write 1 in the 2^3 place. Subtract 8 from 14. 14 - 8 = 6.

8 Step 6 -Continue the process: Identify the next largest power of 2 that fits into the result of the previous step, 6. The next largest power of 2 is 2^2, which is 4. Write 1 in the 2^2 place. Subtract 4 from 6. 6 - 4 = 2.

9 Step 7 -Continue the process: Identify the next largest power of 2 that fits into the result of the previous step, 2. The next largest power of 2 is 2^1, which is 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.

10 Step 8 -Identify the unused place values: In the previous steps, we wrote 1 in the 2^6, 2^5, 2^4, 2^3, 2^2, and 2^1 places. Now, we can just write 0 in the remaining place, which is 2^0. Now, by substituting the values, we get, 0 in the 2^0 place 1 in the 2^1 place 1 in the 2^2 place 1 in the 2^3 place 1 in the 2^4 place 1 in the 2^5 place 1 in the 2^6 place

11 Step 9 -Write the values in reverse order: We now write the numbers upside down to represent 126 in binary. Therefore, 1111110 is 126 in binary.

12 Grouping Method:In this method, we divide the number 126 by 2. Let us see the step-by-step conversion.

13 Step 1 -Divide the given number 126 by 2. 126 / 2 = 63. Here, 63 is the quotient and 0 is the remainder. Step 2 - Divide the previous quotient (63) by 2. 63 / 2 = 31. Here, the quotient is 31 and the remainder is 1.

14 Step 3 -Repeat the previous step. 31 / 2 = 15. Now, the quotient is 15, and 1 is the remainder.

15 Step 4 -Repeat the previous step. 15 / 2 = 7. Here, the quotient is 7, and 1 is the remainder.

16 Step 5 -Repeat the previous step. 7 / 2 = 3. Here, the quotient is 3, and 1 is the remainder.

17 Step 6 -Repeat the previous step. 3 / 2 = 1. Here, the quotient is 1, and 1 is the remainder.

18 Step 7 -Repeat the previous step. 1 / 2 = 0. Here, the remainder is 1. And we stop the<a>division</a>here because the quotient is 0.

19 Step 8 -Write down the remainders from bottom to top. Therefore, 126 (decimal) = 1111110 (binary).