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Original 2026-01-01

Modified 2026-02-28

1 1313 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 1313 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 29 = 512 210 = 1024 Since 1024 is the largest power<a>less than</a>1313, we use it to start.

4 Step 2- Identify the largest power of 2: In the previous step, we stopped at 210 = 1024. This is because we have to identify the largest power of 2, which is less than or equal to the given number, 1313. Since 210 is the number we are looking for, write 1 in the 210 place. Now subtract the value of 210, which is 1024, from 1313. 1313 - 1024 = 289.

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 289. The next largest power of 2 is 28, which is 256. Write 1 in the 28 place. Subtract 256 from 289. 289 - 256 = 33.

6 Step 4- Repeat the process: Continue finding the next largest powers of 2 that fit into the remainder, 33. The powers are 25 = 32 and 20 = 1. Write 1 in the 25 and 20 places. Subtract the corresponding values from the remainder. 33 - 32 = 1. 1 - 1 = 0.

7 Step 5- Fill in the remaining powers: Write 0s in the places that were not used, which are 29, 27, 26, 24, 23, 22, and 21. Now, by substituting the values, we get: 0 in the 29 place 1 in the 28 place 0 in the 27 place 0 in the 26 place 1 in the 25 place 0 in the 24 place 0 in the 23 place 0 in the 22 place 0 in the 21 place 1 in the 20 place

8 Step 6- Write the values in<a>sequence</a>: The binary representation of 1313 is 10100100001.

9 Grouping Method: In this method, we divide the number 1313 by 2. Let us see the step-by-step conversion.

10 Step 1- Divide the given number 1313 by 2. 1313 / 2 = 656 with a remainder of 1.

11 Step 2- Divide the previous quotient (656) by 2. 656 / 2 = 328 with a remainder of 0.

12 Step 3- Repeat the previous step. 328 / 2 = 164 with a remainder of 0.

13 Step 4- Repeat the previous step. 164 / 2 = 82 with a remainder of 0.

14 Step 5- Continue the process until the quotient becomes 0. 82 / 2 = 41 with a remainder of 0. 41 / 2 = 20 with a remainder of 1. 20 / 2 = 10 with a remainder of 0. 10 / 2 = 5 with a remainder of 0. 5 / 2 = 2 with a remainder of 1. 2 / 2 = 1 with a remainder of 0. 1 / 2 = 0 with a remainder of 1.

15 Step 6- Write down the remainders from bottom to top. The binary equivalent of 1313 is 10100100001.