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Original
2026-01-01
Modified
2026-02-28
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<p>1031 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.</p>
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<p>1031 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.</p>
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<p>Expansion Method: Let us see the step-by-step process of converting 1031 using the expansion method.</p>
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<p>Expansion Method: Let us see the step-by-step process of converting 1031 using the expansion method.</p>
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<p><strong>Step 1</strong>- 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.</p>
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<p><strong>Step 1</strong>- 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.</p>
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<p>20 = 1</p>
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<p>20 = 1</p>
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<p>21 = 2</p>
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<p>21 = 2</p>
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<p>22 = 4</p>
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<p>22 = 4</p>
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<p>23 = 8</p>
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<p>23 = 8</p>
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<p>24 = 16</p>
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<p>24 = 16</p>
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<p>25 = 32</p>
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<p>25 = 32</p>
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<p>26 = 64</p>
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<p>26 = 64</p>
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<p>27 = 128</p>
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<p>27 = 128</p>
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<p>28 = 256</p>
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<p>28 = 256</p>
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<p>29 = 512</p>
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<p>29 = 512</p>
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<p>210 = 1024</p>
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<p>210 = 1024</p>
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<p>Since 1024 is<a>greater than</a>1031, we stop at 2^9 = 512.</p>
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<p>Since 1024 is<a>greater than</a>1031, we stop at 2^9 = 512.</p>
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<p><strong>Step 2</strong>- Identify the largest power of 2: In the previous step, we stopped at 29 = 512. 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, 1031. Since 29 is the number we are looking for, write 1 in the 29 place. Now the value of 29, which is 512, is subtracted from 1031. 1031 - 512 = 519.</p>
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<p><strong>Step 2</strong>- Identify the largest power of 2: In the previous step, we stopped at 29 = 512. 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, 1031. Since 29 is the number we are looking for, write 1 in the 29 place. Now the value of 29, which is 512, is subtracted from 1031. 1031 - 512 = 519.</p>
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<p><strong>Step 3</strong>- 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, 519. So, the next largest power of 2 is 28, which is 256. Now, we have to write 1 in the 28 place. And then subtract 256 from 519. 519 - 256 = 263. Repeat the process for powers of 27, 26, 25, 24, and 23 until you reach 0.</p>
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<p><strong>Step 3</strong>- 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, 519. So, the next largest power of 2 is 28, which is 256. Now, we have to write 1 in the 28 place. And then subtract 256 from 519. 519 - 256 = 263. Repeat the process for powers of 27, 26, 25, 24, and 23 until you reach 0.</p>
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<p><strong>Step 4</strong>- Identify the unused place values: In previous steps, we wrote 1s in the places for the powers of 2 that were used. Now, we can just write 0s in the remaining places. Now, by substituting the values, we get: 1 in the 29 place 1 in the 28 place 0 in the 27 place 0 in the 26 place 0 in the 25 place 0 in the 24 place 0 in the 23 place 1 in the 22 place 1 in the 21 place 1 in the 20 place</p>
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<p><strong>Step 4</strong>- Identify the unused place values: In previous steps, we wrote 1s in the places for the powers of 2 that were used. Now, we can just write 0s in the remaining places. Now, by substituting the values, we get: 1 in the 29 place 1 in the 28 place 0 in the 27 place 0 in the 26 place 0 in the 25 place 0 in the 24 place 0 in the 23 place 1 in the 22 place 1 in the 21 place 1 in the 20 place</p>
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<p><strong>Step 5</strong>- Write the values in reverse order: We now write the numbers upside down to represent 1031 in binary. Therefore, 10000000111 is 1031 in binary.</p>
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<p><strong>Step 5</strong>- Write the values in reverse order: We now write the numbers upside down to represent 1031 in binary. Therefore, 10000000111 is 1031 in binary.</p>
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<p>Grouping Method: In this method, we divide the number 1031 by 2. Let us see the step-by-step conversion.</p>
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<p>Grouping Method: In this method, we divide the number 1031 by 2. Let us see the step-by-step conversion.</p>
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<p><strong>Step 1</strong>- Divide the given number 1031 by 2. 1031 / 2 = 515. Here, 515 is the quotient and 1 is the remainder.</p>
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<p><strong>Step 1</strong>- Divide the given number 1031 by 2. 1031 / 2 = 515. Here, 515 is the quotient and 1 is the remainder.</p>
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<p><strong>Step 2</strong>- Divide the previous quotient (515) by 2. 515 / 2 = 257. Here, the quotient is 257 and the remainder is 1.</p>
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<p><strong>Step 2</strong>- Divide the previous quotient (515) by 2. 515 / 2 = 257. Here, the quotient is 257 and the remainder is 1.</p>
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<p><strong>Step 3</strong>- Repeat the previous step. 257 / 2 = 128. Now, the quotient is 128, and 1 is the remainder. Continue dividing until the quotient is 0, then write the remainders from bottom to top.</p>
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<p><strong>Step 3</strong>- Repeat the previous step. 257 / 2 = 128. Now, the quotient is 128, and 1 is the remainder. Continue dividing until the quotient is 0, then write the remainders from bottom to top.</p>
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