Rivalry2

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Original 2026-01-01

Modified 2026-02-28

1 119 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 119 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>119, we stop at 26 = 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, 119. 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 119. 119 - 64 = 55.

14 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, 55. So, the next largest power of 2 is 25, which is less than or equal to 55. Now, we have to write 1 in the 25 place. And then subtract 32 from 55. 55 - 32 = 23.

15 Step 4 -Continue the process: Now, find the largest power of 2 less than or equal to 23, which is 24 = 16. Write 1 in the 24 place and subtract 16 from 23. 23 - 16 = 7.

16 Step 5 -Continue with remaining value: For the remainder 7, the largest power of 2 is 22 = 4. Write 1 in the 22 place and subtract 4 from 7. 7 - 4 = 3. Now, for 3, the largest power of 2 is 21 = 2. Write 1 in the 21 place and subtract 2 from 3. 3 - 2 = 1. Finally, for 1, 20 = 1. Write 1 in the 20 place. We have reached 0, so the conversion process stops here.

17 Step 6 -Write the values in order: We now write the numbers to represent 119 in binary. Therefore, 1110111 is 119 in binary.

18 Grouping Method:In this method, we divide the number 119 by 2. Let us see the step-by-step conversion.

19 Step 1 -Divide the given number 119 by 2. 119 / 2 = 59. Here, 59 is the quotient and 1 is the remainder.

20 Step 2 -Divide the previous quotient (59) by 2. 59 / 2 = 29. Here, the quotient is 29 and the remainder is 1.

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

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

23 Step 5 -Continue the process. 7 / 2 = 3. The quotient is 3, and the remainder is 1. 3 / 2 = 1. The quotient is 1, and the remainder is 1. 1 / 2 = 0. The quotient is 0, and the remainder is 1. We stop the<a>division</a>here because the quotient is 0.

24 Step 6 -Write down the remainders from bottom to top. Therefore, 119 (decimal) = 1110111 (binary).