116 in Binary
2026-02-21 20:30 Diff
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116 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 116 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 116, 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, 116. 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 116. 116 - 64 = 52.

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, 52. So, the next largest power of 2 is 25, which is less than or equal to 52. Now, we have to write 1 in the 25 places. And then subtract 32 from 52. 52 - 32 = 20.

Step 4 - Repeat the process: Continue identifying the largest power of 2 that fits into the remaining number. 24 = 16 is the next power. Write 1 in the 24 place and subtract 16 from 20. 20 - 16 = 4. The next largest power 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.

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

Step 6 - Write the values in reverse order: We now write the numbers upside down to represent 116 in binary. Therefore, 1110100 is 116 in binary.

Grouping Method: In this method, we divide the number 116 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 116 by 2. 116 / 2 = 58. Here, 58 is the quotient, and 0 is the remainder.

Step 2 - Divide the previous quotient (58) by 2. 58 / 2 = 29. Here, the quotient is 29, and the remainder is 0.

Step 3 - Repeat the previous step. 29 / 2 = 14. Now, the quotient is 14, and 1 is the remainder.

Step 4 - Repeat the previous step. 14 / 2 = 7. Now, the quotient is 7, and 0 is the remainder.

Step 5 - Repeat the previous step. 7 / 2 = 3. Now, the quotient is 3, and 1 is the remainder.

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

Step 7 - Repeat the previous step. 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, 116 (decimal) = 1110100 (binary).