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Original 2026-01-01

Modified 2026-02-28

1 239 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 239 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. 20 = 1 21 = 2 22 = 4 23 = 8 24 = 16 25 = 32 26 = 64 27 = 128 28 = 256 Since 256 is<a>greater than</a>239, we stop at 27 = 128.

4 Step 2 -Identify the largest power of 2: In the previous step, we stopped at 27 = 128. This is because we have to identify the largest power of 2, which is<a>less than</a>or equal to the given number, 239. 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 239. 239 - 128 = 111.

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, 111. So, the next largest power of 2 is 26 = 64. Write 1 in the 26 place and subtract 64 from 111. 111 - 64 = 47.

6 Step 4 -Continue the process: Repeat the process of finding the largest power of 2 for the remaining numbers. For 47, the largest power of 2 is 25 = 32. Write 1 in the 25 place. 47 - 32 = 15. For 15, the largest power of 2 is 23 = 8. Write 1 in the 23 place. 15 - 8 = 7. For 7, the largest power of 2 is 22 = 4. Write 1 in the 22 place. 7 - 4 = 3. For 3, the largest power of 2 is 21 = 2. Write 1 in the 21 place. 3 - 2 = 1. For 1, the largest power of 2 is 20 = 1. Write 1 in the 20 place. 1 - 1 = 0.

7 Step 5 -Write the values in reverse order: We now write the numbers upside down to represent 239 in binary. Therefore, 11101111 is 239 in binary.

8 Grouping Method:In this method, we divide the number 239 by 2. Let us see the step-by-step conversion.

9 Step 1 -Divide the given number 239 by 2. 239 / 2 = 119. Here, 119 is the quotient and 1 is the remainder.

10 Step 2 -Divide the previous quotient (119) by 2. 119 / 2 = 59. Here, the quotient is 59 and the remainder is 1.

11 Step 3 -Repeat the previous step. 59 / 2 = 29. Now, the quotient is 29 and 1 is the remainder.

12 Step 4 -Repeat the previous step. 29 / 2 = 14. Here, the quotient is 14 and 1 is the remainder.

13 Step 5 -Continue the process: 14 / 2 = 7. Quotient is 7, remainder is 0. 7 / 2 = 3. Quotient is 3, remainder is 1. 3 / 2 = 1. Quotient is 1, remainder is 1. 1 / 2 = 0. Quotient is 0, remainder is 1.

14 Step 6 -Write down the remainders from bottom to top. Therefore, 239 (decimal) = 11101111 (binary).