Rivalry2

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Original 2026-01-01

Modified 2026-02-28

1 224 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. Expansion Method: Let us see the step-by-step process of converting 224 using the expansion method.

2 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.

3 20 = 1

4 21 = 2

5 22 = 4

6 23 = 8

7 24 = 16

8 25 = 32

9 26 = 64

10 27 = 128

11 28 = 256

12 Since 256 is<a>greater than</a>224, we stop at 27 = 128.

13 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, 224.

14 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 224. 224 - 128 = 96

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, 96.

16 So, the next largest power of 2 is 26, which is 64. Now, we have to write 1 in the 26 places. And then subtract 64 from 96. 96 - 64 = 32

17 Step 4 -Identify the next largest power of 2: Now, we need to find the power of 2 that fits into 32. That would be 25. Write 1 in the 25 places, and subtract 32 from 32. 32 - 32 = 0

18 Step 5 -Identify the unused place values: In step 2, step 3, and step 4, we wrote 1 in the 27, 26, and 25 places. Now, we can just write 0s in the remaining places, which are 24, 23, 22, 21, and 20.

19 Now, by substituting the values, we get, 0 in the 20 place 0 in the 21 place 0 in the 22 place 0 in the 23 place 0 in the 24 place 1 in the 25 place 1 in the 26 place 1 in the 27 place

20 Step 6 -Write the values in reverse order: We now write the numbers upside down to represent 224 in binary. Therefore, 11100000 is 224 in binary. Grouping Method: In this method, we divide the number 224 by 2. Let us see the step-by-step conversion.

21 Step 1 -Divide the given number 224 by 2. 224 / 2 = 112. Here, 112 is the quotient and 0 is the remainder. Step 2 - Divide the previous quotient (112) by 2. 112 / 2 = 56.

22 Here, the quotient is 56 and the remainder is 0. Step 3 - Repeat the previous step. 56 / 2 = 28. Now, the quotient is 28, and 0 is the remainder.

23 Step 4 -Repeat the previous step. 28 / 2 = 14. Here, the quotient is 14, and the remainder is 0. Step 5 - Repeat the previous step. 14 / 2 = 7.

24 Here, the quotient is 7, and the remainder is 0.

25 Step 6 -Repeat the previous step. 7 / 2 = 3. Here, the quotient is 3, and the remainder is 1. Step 7 - Repeat the previous step. 3 / 2 = 1.

26 Here, the quotient is 1, and the remainder is 1.

27 Step 8 -Repeat the previous step. 1 / 2 = 0.

28 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, 224 (decimal) = 11100000 (binary).