Rivalry2

HTML Diff

0 added 0 removed

Original 2026-01-01

Modified 2026-02-28

1 104 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 104 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.

4 20 = 1

5 21 = 2

6 22 = 4

7 23 = 8

8 24 = 16

9 25 = 32

10 26 = 64

11 27 = 128

12 Since 128 is<a>greater than</a>104, we stop at 26 = 64.

13 Step 2 -Identify the largest power of 2: In the previous step, we stopped at 26 = 64. This is because we have to identify the largest power of 2, which is<a>less than</a>or equal to the given number, 104. Since 278 is the number we are looking for, write 1 in the 26 place. Now the value of 26, which is 64, is subtracted from 104. 104 - 64 = 40.

14 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, 40. So, the next largest power of 2 is 25 = 32, which is less than or equal to 40. Now, we have to write 1 in the 25 places. And then subtract 32 from 40. 40 - 32 = 8.

15 Step 4 -Identify the next largest power of 2: The next largest power of 2 is 23 = 8, which is equal to 8. Now, write 1 in the 23 place. And subtract 8 from 8. 8 - 8 = 0. We need to stop the process here since the<a>remainder</a>is 0.

16 Step 5 -Identify the unused place values: In steps 2, 3, and 4, we wrote 1 in the 26, 2`````````````5, and 23 places. Now, we can just write 0s in the remaining places, which are 24, 22, 21, and 20. Now, by substituting the values, we get, 0 in the 20 place 0 in the 21 place 0 in the 22 place 1 in the 23 place 0 in the 24 place 1 in the 25 place 1 in the 26 place

17 Step 6 -Write the values in reverse order: We now write the numbers upside down to represent 104 in binary. Therefore, 1101000 is 104 in binary.

18 Grouping Method:In this method, we divide the number 104 by 2. Let us see the step-by-step conversion.

19 Step 1 -Divide the given number 104 by 2. 104 / 2 = 52. Here, 52 is the quotient and 0 is the remainder.

20 Step 2 -Divide the previous quotient (52) by 2. 52 / 2 = 26. Here, the quotient is 26 and the remainder is 0.

21 Step 3 -Repeat the previous step. 26 / 2 = 13. Now, the quotient is 13, and 0 is the remainder.

22 Step 4 -Repeat the previous step. 13 / 2 = 6. The quotient is 6 and the remainder is 1.

23 Step 5 -Repeat the previous step. 6 / 2 = 3. Here, the quotient is 3 and the remainder is 0.

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

25 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.

26 Step 8 -Write down the remainders from bottom to top. Therefore, 104 (decimal) = 1101000 (binary).