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Original 2026-01-01

Modified 2026-02-28

1 65535 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 65535 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 ... 215 = 32768 216 = 65536 Since 65536 is<a>greater than</a>65535, we stop at 215 = 32768.

4 Step 2 -Identify the largest power of 2: In the previous step, we stopped at 215 = 32768. 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, 65535. Since 215 is the number we are looking for, write 1 in the 215 place. Now the value of 215, which is 32768, is subtracted from 65535. 65535 - 32768 = 32767.

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, 32767. So, the next largest power of 2 is 214, which is 16384. Now, we have to write 1 in the 214 place. And then subtract 16384 from 32767. 32767 - 16384 = 16383. The process continues until all place values are filled. Finally, by substituting the values, we get, 1111111111111111.

6 Grouping Method:In this method, we divide the number 65535 by 2. Let us see the step-by-step conversion.

7 Step 1 -Divide the given number 65535 by 2. 65535 / 2 = 32767. Here, 32767 is the quotient and 1 is the remainder.

8 Step 2 -Divide the previous quotient (32767) by 2. 32767 / 2 = 16383. Here, the quotient is 16383 and the remainder is 1.

9 Step 3 -Repeat the previous step for all subsequent quotients until the quotient is 0.

10 Step 4 -Write down the remainders from bottom to top. Therefore, 65535 (decimal) = 1111111111111111 (binary).