Rivalry2

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Original 2026-01-01

Modified 2026-02-28

1 57 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 57 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. 2^0 = 1 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16<a>2^5</a>= 32 2^6 = 64 Since 64 is<a>greater than</a>57, we stop at 2^5 = 32.

4 Step 2 -Identify the largest power of 2: In the previous step, we stopped at 2^5 = 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, 57. Since 2^5 is the number we are looking for, write 1 in the 2^5 place. Now the value of 2^5, which is 32, is subtracted from 57. 57 - 32 = 25.

5 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, 25. So, the next largest power of 2 is 2^4, which is less than or equal to 25. Now, we have to write 1 in the 2^4 places. And then subtract 16 from 25. 25 - 16 = 9.

6 Step 4 -Identify the next largest power of 2: Now, we find the largest power of 2 that fits into 9. The next largest power of 2 is 2^3, which is less than or equal to 9. Write 1 in the 2^3 place and subtract 8 from 9. 9 - 8 = 1.

7 Step 5 -Identify the next largest power of 2: The largest power of 2 that fits into 1 is 2^0. Write 1 in the 2^0 place and subtract 1 from 1. 1 - 1 = 0. We stop the process here since the remainder is 0.

8 Step 6 -Identify the unused place values: In the steps above, we wrote 1 in the 2^5, 2^4, 2^3, and 2^0 places. Now, we can just write 0s in the remaining places, which are 2^2 and 2^1. Now, by substituting the values, we get, 1 in the 2^0 place 0 in the 2^1 place 0 in the 2^2 place 1 in the 2^3 place 1 in the 2^4 place 1 in the 2^5 place

9 Step 7 -Write the values in reverse order: We now write the numbers upside down to represent 57 in binary. Therefore, 111001 is 57 in binary.

10 Grouping Method:In this method, we divide the number 57 by 2. Let us see the step-by-step conversion.

11 Step 1 -Divide the given number 57 by 2. 57 / 2 = 28. Here, 28 is the quotient and 1 is the remainder. Step 2 - Divide the previous quotient (28) by 2. 28 / 2 = 14. Here, the quotient is 14 and the remainder is 0.

12 Step 3 -Repeat the previous step. 14 / 2 = 7. Now, the quotient is 7, and 0 is the remainder. Step 4 - Repeat the previous step. 7 / 2 = 3. Here, the remainder is 1.

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

14 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.

15 Step 7 -Write down the remainders from bottom to top. Therefore, 57 (decimal) = 111001 (binary).