Rivalry2

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Original 2026-01-01

Modified 2026-02-21

1 88 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 88 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>88, we stop at 2^6 = 64.

13 Step 2 -Identify the largest power of 2: In the previous step, we stopped at 2^6 = 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, 88. Since 2^6 is the number we are looking for, write 1 in the 2^6 place. Now the value of 2^6, which is 64, is subtracted from 88. 88 - 64 = 24.

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, 24. So, the next largest power of 2 is 2^4, which is less than or equal to 24. Now, we have to write 1 in the 2^4 place. And then subtract 16 from 24. 24 - 16 = 8.

15 Step 4 -Identify the next largest power of 2: We need to find the largest power of 2 that fits into the result of the previous step, 8. So, the next largest power of 2 is 2^3, which is equal to 8. Now, we write 1 in the 2^3 place. And then subtract 8 from 8. 8 - 8 = 0. We need to stop the process here since the remainder is 0.

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

17 Step 6 -Write the values in reverse order: We now write the numbers upside down to represent 88 in binary. Therefore, 1011000 is 88 in binary.

18 Grouping Method:In this method, we divide the number 88 by 2. Let us see the step-by-step conversion.

19 Step 1 -Divide the given number 88 by 2. 88 / 2 = 44. Here, 44 is the quotient and 0 is the remainder.

20 Step 2 -Divide the previous quotient (44) by 2. 44 / 2 = 22. Here, the quotient is 22 and the remainder is 0.

21 Step 3 -Repeat the previous step. 22 / 2 = 11. Now, the quotient is 11, and 0 is the remainder.

22 Step 4 -Repeat the previous step. 11 / 2 = 5. Here, the remainder is 1.

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

24 Step 6 -Repeat the previous step. 2 / 2 = 1. Here, the remainder is 0.

25 Step 7 -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.

26 Step 8 -Write down the remainders from bottom to top. Therefore, 88 (decimal) = 1011000 (binary).