Rivalry2

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Original 2026-01-01

Modified 2026-02-28

1 120 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.

2 Expansion Method: Let us see the step-by-step process of converting 120 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.

4 20 = 1

5 21 = 2

6 22 = 4

7 23 = 8

8 24 = 16

9 25 = 32

10 26 = 64

11 27 = 128

12 Since 128 is<a>greater than</a>120, we stop at 2^6 = 64.

13 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, 120.

14 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.

15 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.

16 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.

17 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.

18 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

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

20 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.

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

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

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

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

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

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

27 Step 7 -Divide the remaining quotient. 1 / 2 = 0. Here, the remainder is 1. And we stop the<a>division</a>here because the quotient is 0.

28 Step 8 -Write down the remainders from bottom to top. Therefore, 120 (decimal) = 1111000 (binary).