Rivalry2

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Original 2026-01-01

Modified 2026-02-28

1 53 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 53 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 Since 64 is<a>greater than</a>53, we stop at 25 = 32.

12 Step 2- Identify the largest power of 2: In the previous step, we stopped at 25 = 32. 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, 53. Since 25 is the number we are looking for, write 1 in the 25 place. Now the value of 25, which is 32, is subtracted from 53. 53 - 32 = 21.

13 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, which is 16. Now, we have to write 1 in the 24 places. And then subtract 16 from 21. 21 - 16 = 5.

14 Step 4- Identify the next largest power of 2: Now, we find 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.

15 Step 5- Identify the next largest power of 2: Now, we find the largest power of 2 that fits into 1, which is 20 = 1. Write 1 in the 20 place and subtract 1 from 1. 1 - 1 = 0. We need to stop the process here since the remainder is 0.

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

17 Step 7- Write the values in reverse order: We now write the numbers upside down to represent 53 in binary. Therefore, 110101 is 53 in binary.

18 Grouping Method: In this method, we divide the number 53 by 2. Let us see the step-by-step conversion.

19 Step 1- Divide the given number 53 by 2. 53 / 2 = 26. Here, 26 is the quotient and 1 is the remainder.

20 Step 2- Divide the previous quotient (26) by 2. 26 / 2 = 13. Here, the quotient is 13 and the remainder is 0.

21 Step 3- Repeat the previous step. 13 / 2 = 6. Now, the quotient is 6, and 1 is the remainder.

22 Step 4- Repeat the previous step. 6 / 2 = 3. Here, the quotient is 3, and 0 is the remainder.

23 Step 5- Repeat the previous step. 3 / 2 = 1. Here, the quotient is 1, and 1 is the remainder.

24 Step 6- 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.

25 Step 7- Write down the remainders from bottom to top. Therefore, 53 (decimal) = 110101 (binary).