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Original 2026-01-01

Modified 2026-02-28

1 102 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 102 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. 20 = 1 21 = 2 22 = 4 23 = 8 24 = 16 25 = 32 26 = 64 27 = 128 Since 128 is<a>greater than</a>102, we stop at 26 = 64.

4 Step 2 -Identify the largest power of 2: In the previous step, we stopped at 26 = 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, 102. Since 26 is the number we are looking for, write 1 in the 26 place. Now the value of 26, which is 64, is subtracted from 102. 102 - 64 = 38.

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, 38. So, the next largest power of 2 is 25 = 32. Now, we have to write 1 in the 25 place. And then subtract 32 from 38. 38 - 32 = 6.

6 Step 4 -Continue the process: The next largest power for 6 is 22 = 4. Write 1 in the 22 place and subtract 4 from 6. 6 - 4 = 2.

7 Step 5 - Final Step:The next largest power is 21 = 2. Write 1 in the 21 place and subtract 2 from 2. 2 - 2 = 0. We need to stop the process here since the remainder is 0.

8 Step 6 -Identify the unused place values: In previous steps, we wrote 1 in the 26, 25, 22, and 21 places. Now, we can just write 0s in the remaining places, which are 24, 23, and 20. Now, by substituting the values, we get: 0 in the 20 place 1 in the 21 place 1 in the 22 place 0 in the 23 place 0 in the 24 place 1 in the 25 place 1 in the 26 place

9 Step 7 -Write the values in reverse order: We now write the numbers upside down to represent 102 in binary. Therefore, 1100110 is 102 in binary.

10 Grouping Method:In this method, we divide the number 102 by 2. Let us see the step-by-step conversion.

11 Step 1 -Divide the given number 102 by 2. 102 / 2 = 51. Here, 51 is the quotient and 0 is the remainder.

12 Step 2 -Divide the previous quotient (51) by 2. 51 / 2 = 25. Here, the quotient is 25 and the remainder is 1.

13 Step 3 -Divide the previous quotient (25) by 2. 25 / 2 = 12. Here, the quotient is 12 and the remainder is 1.

14 Step 4 -Divide the previous quotient (12) by 2. 12 / 2 = 6. Here, the quotient is 6 and the remainder is 0.

15 Step 5 -Divide the previous quotient (6) by 2. 6 / 2 = 3. Here, the quotient is 3 and the remainder is 0.

16 Step 6 -Divide the previous quotient (3) by 2. 3 / 2 = 1. Here, the quotient is 1 and the remainder is 1.

17 Step 7 -Divide the previous quotient (1) by 2. 1 / 2 = 0. Here, the remainder is 1. And we stop the<a>division</a>here because the quotient is 0.

18 Step 8 -Write down the remainders from bottom to top. Therefore, 102 (decimal) = 1100110 (binary).