102 in Binary
2026-02-28 11:19 Diff
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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.

Expansion Method: Let us see the step-by-step process of converting 102 using the expansion method.

Step 1 - Figure out the place values: In the binary system, each place value is a power 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 greater than 102, we stop at 26 = 64.

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 less than 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.

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.

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.

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.

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

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.

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

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

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

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

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

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

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

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

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