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Original 2026-01-01

Modified 2026-02-28

1 108 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 108 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>108, we stop at 26 = 64.

13 Step 2- Identify the largest power of 2:

14 In the previous step, we stopped at 26 = 64.

15 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, 108.

16 Since 26 is the number we are looking for, write 1 in the 26 place.

17 Now the value of 26, which is 64, is subtracted from 108. 108 - 64 = 44.

18 Step 3 - Identify the next largest power of 2:

19 In this step, we need to find the largest power of 2 that fits into the result of the previous step, 44.

20 So, the next largest power of 2 is 25, which is equal to 32.

21 Now, we have to write 1 in the 25 place.

22 And then subtract 32 from 44. 44 - 32 = 12.

23 Step 4- Identify the next largest power of 2: The next largest power of 2 fitting into 12 is 23 = 8. Write 1 in the 23 place and subtract 8 from 12. 12 - 8 = 4.

24 Step 5- Identify the next largest power of 2: The next largest power of 2 fitting into 4 is 22 = 4. Write 1 in the 22 place and subtract 4 from 4. 4 - 4 = 0. We need to stop the process here since the remainder is 0.

25 Step 6- Identify the unused place values: In steps 2, 3, 4, and 5, we wrote 1 in the 26, 25, 23, and 22 places.

26 Now, we can just write 0s in the remaining places, which are 24, 21, and 20.

27 Now, by substituting the values, we get, 0 in the 20 place 0 in the 21 place 1 in the 22 place 1 in the 23 place 0 in the 24 place 1 in the 25 place 1 in the 26 place

28 Step 7- Write the values in reverse order: We now write the numbers upside down to represent 108 in binary. Therefore, 1101100 is 108 in binary.

29 Grouping Method: In this method, we divide the number 108 by 2. Let us see the step-by-step conversion.

30 Step 1- Divide the given number 108 by 2. 108 / 2 = 54. Here, 54 is the quotient and 0 is the remainder.

31 Step 2- Divide the previous quotient (54) by 2. 54 / 2 = 27. Here, the quotient is 27 and the remainder is 0.

32 Step 3- Repeat the previous step. 27 / 2 = 13. Now, the quotient is 13, and 1 is the remainder.

33 Step 4- Repeat the previous step. 13 / 2 = 6. Here, the remainder is 1.

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

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

36 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.

37 Step 8- Write down the remainders from bottom to top.

38 Therefore, 108 (decimal) = 1101100 (binary).