Rivalry2

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Original 2026-01-01

Modified 2026-02-28

1 165 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 165 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 28 = 256

13 Since 256 is<a>greater than</a>165, we stop at 27 = 128.

14 Step 2- Identify the largest power of 2: In the previous step, we stopped at 27 = 128. 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, 165. Since 27 is the number we are looking for, write 1 in the 27 place. Now the value of 27, which is 128, is subtracted from 165. 165 - 128 = 37.

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, 37. So, the next largest power of 2 is 25, which is less than or equal to 37. Now, we have to write 1 in the 25 place. And then subtract 32 from 37. 37 - 32 = 5.

16 Step 4- 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, 5. So, the next largest power of 2 is 22, which is less than or equal to 5. Now, we have to write 1 in the 22 place. And then subtract 4 from 5. 5 - 4 = 1.

17 Step 5- 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, 1. So, the next largest power of 2 is 20, which is less than or equal to 1. Now, we have to write 1 in the 20 place. And then subtract 1 from 1. 1 - 1 = 0. We need to stop the process here since the remainder is 0.

18 Step 6- Identify the unused place values: In previous steps, we wrote 1 in the 27, 25, 22, and 20 places. Now, we can just write 0s in the remaining places, which are 26, 24, 23, and 21. Now, by substituting the values, we get: 0 in the 26 place 1 in the 25 place 0 in the 24 place 0 in the 23 place 1 in the 22 place 0 in the 21 place 1 in the 20 place

19 Step 7- Write the values in reverse order: We now write the numbers upside down to represent 165 in binary. Therefore, 10100101 is 165 in binary.

20 Grouping Method: In this method, we divide the number 165 by 2. Let us see the step-by-step conversion.

21 Step 1- Divide the given number 165 by 2. 165 / 2 = 82. Here, 82 is the quotient and 1 is the remainder.

22 Step 2- Divide the previous quotient (82) by 2. 82 / 2 = 41. Here, the quotient is 41 and the remainder is 0.

23 Step 3- Repeat the previous step. 41 / 2 = 20. Now, the quotient is 20, and 1 is the remainder.

24 Step 4- Repeat the previous step. 20 / 2 = 10. Here, the quotient is 10, and 0 is the remainder.

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

26 Step 6- Repeat the previous step. 5 / 2 = 2. Here, the quotient is 2, and 1 is the remainder.

27 Step 7- Repeat the previous step. 2 / 2 = 1. Here, the quotient is 1, and 0 is the remainder.

28 Step 8- Repeat the previous step. 1 / 2 = 0. Here, the remainder is 1. And we stop the<a>division</a>here because the quotient is 0.

29 Step 9- Write down the remainders from bottom to top. Therefore, 165 (decimal) = 10100101 (binary).