85 in Binary
2026-02-28 14:06 Diff
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85 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 85 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 85, 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, 85. 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 85. 85 - 64 = 21.

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, 21. So, the next largest power of 2 is 24 = 16, which is less than or equal to 21. Now, we have to write 1 in the 24 place. And then subtract 16 from 21. 21 - 16 = 5.

Step 4 - Repeat the process: We continue by identifying the largest power of 2 that fits into 5, which is 22 = 4. Write 1 in the 22 place and subtract 4 from 5. 5 - 4 = 1.

Step 5 - Write the remaining values: 1 is equal to 20, so write 1 in the 20 place. For all unused places, write 0. Combine the values to get the binary number: 1 in the 26 place 0 in the 25 place 1 in the 24 place 0 in the 23 place 1 in the 22 place 0 in the 21 place 1 in the 20 place Therefore, 1010101 is 85 in binary.

Grouping Method: In this method, we divide the number 85 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 85 by 2. 85 / 2 = 42. Here, 42 is the quotient and 1 is the remainder.

Step 2 - Divide the previous quotient (42) by 2. 42 / 2 = 21. Here, the quotient is 21 and the remainder is 0.

Step 3 - Repeat the previous step. 21 / 2 = 10. Now, the quotient is 10, and 1 is the remainder.

Step 4 - Repeat the previous step. 10 / 2 = 5. The quotient is 5, and the remainder is 0.

Step 5 - Continue the process. 5 / 2 = 2. The quotient is 2, and 1 is the remainder.

Step 6 - Continue the process. 2 / 2 = 1. The quotient is 1, and 0 is the remainder.

Step 7 - Final step. 1 / 2 = 0. 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, 85 (decimal) = 1010101 (binary).