120 in Binary
2026-02-28 17:59 Diff
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120 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 120 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 120, we stop at 2^6 = 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, 120.

Since 26 is the number we are looking for, write 1 in the 2^6 place. Now the value of 26, which is 64, is subtracted from 120. 120 - 64 = 56.

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, 56. 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 56. 56 - 32 = 24.

Step 4 - Identify the next largest power of 2: Repeat the process for 24. The next largest power of 2 is 24 = 16. Write 1 in the 24 place and subtract 16 from 24. 24 - 16 = 8.

Step 5 - Identify the next largest power of 2: For 8, the largest power is 23 = 8. Write 1 in the 23 place and subtract 8 from 8. 8 - 8 = 0. We need to stop the process here since the remainder is 0.

Step 6 - Identify the unused place values: In steps 2, 3, 4, and 5, we wrote 1 in the 26, 25, 24, and 23 places. Now, we can just write 0s in the remaining places, which are 22, 21, and 20. Now, by substituting the values, we get: 0 in the 22 place 0 in the 21 place 0 in the 20 place

Step 7 - Write the values in reverse order: We now write the numbers upside down to represent 120 in binary.

Therefore, 1111000 is 120 in binary. Grouping Method: In this method, we divide the number 120 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 120 by 2. 120 / 2 = 60. Here, 60 is the quotient and 0 is the remainder.

Step 2 - Divide the previous quotient (60) by 2. 60 / 2 = 30. Here, the quotient is 30 and the remainder is 0.

Step 3 - Repeat the previous step. 30 / 2 = 15. Now, the quotient is 15, and 0 is the remainder.

Step 4 - Repeat the previous step. 15 / 2 = 7. Here, the remainder is 1.

Step 5 - Continue the process. 7 / 2 = 3. Here, the remainder is 1.

Step 6 - Continue the process. 3 / 2 = 1. Here, the remainder is 1.

Step 7 - Divide the remaining quotient. 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, 120 (decimal) = 1111000 (binary).