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Original 2026-01-01

Modified 2026-02-28

1 129 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 <h3>Expansion Method:</h3>

3 Let us see the step-by-step process of converting 129 using the expansion method.

4 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.

5 20 = 1

6 21 = 2

7 22 = 4

8 23 = 8

9 24 = 16

10 25 = 32

11 26 = 64

12 27 = 128

13 28 = 256

14 Since 256 is<a>greater than</a>129, we stop at 27 = 128.

15 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, 129. 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 129. 129 - 128 = 1.

16 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, 1. So, the next largest power of 2 is 2^0, which is less than or equal to 1 (in this case equal). Now, we have to write 1 in the 2^0 place. And then subtract 1 from 1. 1 - 1 = 0. We need to stop the process here since the remainder is 0.

17 Step 4 -Identify the unused place values: In step 2 and step 3, we wrote 1 in the 2^7 and 2^0 places. Now, we can just write 0s in the remaining places, which are 2^1 to 2^6. Now, by substituting the values, we get, 1 in the 2^7 place 0 in the 2^6 place 0 in the<a>2^5</a>place 0 in the 2^4 place 0 in the 2^3 place 0 in the 2^2 place 0 in the 2^1 place 1 in the 2^0 place

18 Step 5 -Write the values in reverse order: We now write the numbers upside down to represent 129 in binary. Therefore, 10000001 is 129 in binary.

19 <h3>Grouping Method:</h3>

20 In this method, we divide the number 129 by 2. Let us see the step-by-step conversion.

21 Step 1 -Divide the given number 129 by 2. 129 / 2 = 64. Here, 64 is the quotient and 1 is the remainder.

22 Step 2 -Divide the previous quotient (64) by 2. 64 / 2 = 32. Here, the quotient is 32 and the remainder is 0. Step 3 - Repeat the previous step. 32 / 2 = 16. Now, the quotient is 16, and 0 is the remainder.

23 Step 4 -Repeat the previous step. 16 / 2 = 8. Here, the quotient is 8, and 0 is the remainder.

24 Step 5 -Repeat the previous step. 8 / 2 = 4. Here, the quotient is 4, and 0 is the remainder.

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

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

27 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.

28 Step 9 -Write down the remainders from bottom to top. Therefore, 129 (decimal) = 10000001 (binary).