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Original
2026-01-01
Modified
2026-02-28
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<p>17 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>17 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 17 using the expansion method.</p>
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<p>Expansion Method: Let us see the step-by-step process of converting 17 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 Since 16 is<a>less than</a>17, we stop at 24 = 16.</p>
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<p>24 = 16 Since 16 is<a>less than</a>17, we stop at 24 = 16.</p>
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<p><strong>Step 2</strong>- Identify the largest power of 2: In the previous step, we stopped at 24 = 16. This is because we have to identify the largest power of 2, which is less than or equal to the given number, 17. Since 24 is the number we are looking for, write 1 in the 24 place. Now the value of 24, which is 16, is subtracted from 17. 17 - 16 = 1.</p>
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<p><strong>Step 2</strong>- Identify the largest power of 2: In the previous step, we stopped at 24 = 16. This is because we have to identify the largest power of 2, which is less than or equal to the given number, 17. Since 24 is the number we are looking for, write 1 in the 24 place. Now the value of 24, which is 16, is subtracted from 17. 17 - 16 = 1.</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, 1. The next largest power of 2 that is less than or equal to 1 is 20. Now, we have to write 1 in the 20 place. And then subtract 1 from 1. 1 - 1 = 0. We need to stop the process here since the remainder is 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, 1. The next largest power of 2 that is less than or equal to 1 is 20. Now, we have to write 1 in the 20 place. And then subtract 1 from 1. 1 - 1 = 0. We need to stop the process here since the remainder is 0.</p>
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<p><strong>Step 4</strong>- Identify the unused place values: In step 2 and step 3, we wrote 1 in the 24 and 20 places. Now, we can just write 0s in the remaining places, which are 21, 22, and 23. Now, by substituting the values, we get: 1 in the 24 place 0 in the 23 place 0 in the 22 place 0 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 step 2 and step 3, we wrote 1 in the 24 and 20 places. Now, we can just write 0s in the remaining places, which are 21, 22, and 23. Now, by substituting the values, we get: 1 in the 24 place 0 in the 23 place 0 in the 22 place 0 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 17 in binary. Therefore, 10001 is 17 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 17 in binary. Therefore, 10001 is 17 in binary.</p>
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<p>Grouping Method: In this method, we divide the number 17 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 17 by 2. Let us see the step-by-step conversion.</p>
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<p><strong>Step 1</strong>- Divide the given number 17 by 2. 17 / 2 = 8. Here, 8 is the quotient and 1 is the remainder.</p>
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<p><strong>Step 1</strong>- Divide the given number 17 by 2. 17 / 2 = 8. Here, 8 is the quotient and 1 is the remainder.</p>
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<p><strong>Step 2</strong>- Divide the previous quotient (8) by 2. 8 / 2 = 4. Here, the quotient is 4 and the remainder is 0.</p>
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<p><strong>Step 2</strong>- Divide the previous quotient (8) by 2. 8 / 2 = 4. Here, the quotient is 4 and the remainder is 0.</p>
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<p><strong>Step 3</strong>- Repeat the previous step. 4 / 2 = 2. Now, the quotient is 2, and 0 is the remainder.</p>
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<p><strong>Step 3</strong>- Repeat the previous step. 4 / 2 = 2. Now, the quotient is 2, and 0 is the remainder.</p>
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<p><strong>Step 4</strong>- Repeat the previous step. 2 / 2 = 1. Here, the quotient is 1, and 0 is the remainder.</p>
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<p><strong>Step 4</strong>- Repeat the previous step. 2 / 2 = 1. Here, the quotient is 1, and 0 is the remainder.</p>
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<p><strong>Step 5</strong>- 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.</p>
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<p><strong>Step 5</strong>- 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.</p>
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<p><strong>Step 6</strong>- Write down the remainders from bottom to top. Therefore, 17 (decimal) = 10001 (binary).</p>
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<p><strong>Step 6</strong>- Write down the remainders from bottom to top. Therefore, 17 (decimal) = 10001 (binary).</p>
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