Rivalry2

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Original 2026-01-01

Modified 2026-02-28

1 124 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 124 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>124, 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, 124. 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 124. 124 - 64 = 60.

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, 60. So, the next largest power of 2 is 2^5, which is less than or equal to 60. Now, we have to write 1 in the 2^5 place. And then subtract 32 from 60. 60 - 32 = 28.

6 Step 4 - Repeat the process: Now, we find the largest power of 2 that fits into 28, which is 2^4. Write 1 in the 2^4 place and subtract 16 from 28. 28 - 16 = 12.

7 Step 5 - Repeat the previous step: Now, find the largest power of 2 that fits into 12, which is 2^3. Write 1 in the 2^3 place and subtract 8 from 12. 12 - 8 = 4.

8 Step 6 - Repeat the process: Now, find the largest power of 2 that fits into 4, which is 2^2. Write 1 in the 2^2 place and subtract 4 from 4. 4 - 4 = 0. We need to stop the process here since the remainder is 0.

9 Step 7 - Identify the unused place values: In steps 2 to 6, we wrote 1 in the 2^6, 2^5, 2^4, 2^3, and 2^2 places. Now, we can just write 0s in the remaining places, which are 2^1 and 2^0. Now, by substituting the values, we get, 0 in the 2^0 place 0 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

10 Step 8 - Write the values in reverse order: We now write the numbers upside down to represent 124 in binary. Therefore, 1111100 is 124 in binary.

11 Grouping Method:In this method, we divide the number 124 by 2. Let us see the step-by-step conversion.

12 Step 1 - Divide the given number 124 by 2. 124 / 2 = 62. Here, 62 is the quotient and 0 is the remainder.

13 Step 2 - Divide the previous quotient (62) by 2. 62 / 2 = 31. Here, the quotient is 31 and the remainder is 0.

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. The quotient is 3, and the remainder is 1.

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

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, 124 (decimal) = 1111100 (binary).