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Original
2026-01-01
Modified
2026-02-28
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<p>85 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>85 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 85 using the expansion method.</p>
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<p>Expansion Method: Let us see the step-by-step process of converting 85 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>Since 128 is<a>greater than</a>85, we stop at 26 = 64.</p>
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<p>Since 128 is<a>greater than</a>85, we stop at 26 = 64.</p>
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<p><strong>Step 2</strong>- Identify the largest power of 2: In the previous step, we stopped at 26 = 64. 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, 85. Since 26 is the number we are looking for, write 1 in the 26 place. Now the value of 26, which is 64, is subtracted from 85. 85 - 64 = 21.</p>
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<p><strong>Step 2</strong>- Identify the largest power of 2: In the previous step, we stopped at 26 = 64. 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, 85. Since 26 is the number we are looking for, write 1 in the 26 place. Now the value of 26, which is 64, is subtracted from 85. 85 - 64 = 21.</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, 21. So, the next largest power of 2 is 24 = 16, which is less than or equal to 21. Now, we have to write 1 in the 24 place. And then subtract 16 from 21. 21 - 16 = 5.</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, 21. So, the next largest power of 2 is 24 = 16, which is less than or equal to 21. Now, we have to write 1 in the 24 place. And then subtract 16 from 21. 21 - 16 = 5.</p>
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<p><strong>Step 4</strong>- Repeat the process: We continue by identifying the largest power of 2 that fits into 5, which is 22 = 4. Write 1 in the 22 place and subtract 4 from 5. 5 - 4 = 1.</p>
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<p><strong>Step 4</strong>- Repeat the process: We continue by identifying the largest power of 2 that fits into 5, which is 22 = 4. Write 1 in the 22 place and subtract 4 from 5. 5 - 4 = 1.</p>
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<p><strong>Step 5</strong>- Write the remaining values: 1 is equal to 20, so write 1 in the 20 place. For all unused places, write 0. Combine the values to get the binary number: 1 in the 26 place 0 in the 25 place 1 in the 24 place 0 in the 23 place 1 in the 22 place 0 in the 21 place 1 in the 20 place Therefore, 1010101 is 85 in binary.</p>
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<p><strong>Step 5</strong>- Write the remaining values: 1 is equal to 20, so write 1 in the 20 place. For all unused places, write 0. Combine the values to get the binary number: 1 in the 26 place 0 in the 25 place 1 in the 24 place 0 in the 23 place 1 in the 22 place 0 in the 21 place 1 in the 20 place Therefore, 1010101 is 85 in binary.</p>
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<p>Grouping Method: In this method, we divide the number 85 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 85 by 2. Let us see the step-by-step conversion.</p>
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<p><strong>Step 1</strong>- Divide the given number 85 by 2. 85 / 2 = 42. Here, 42 is the quotient and 1 is the<a>remainder</a>.</p>
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<p><strong>Step 1</strong>- Divide the given number 85 by 2. 85 / 2 = 42. Here, 42 is the quotient and 1 is the<a>remainder</a>.</p>
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<p><strong>Step 2</strong>- Divide the previous quotient (42) by 2. 42 / 2 = 21. Here, the quotient is 21 and the remainder is 0.</p>
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<p><strong>Step 2</strong>- Divide the previous quotient (42) by 2. 42 / 2 = 21. Here, the quotient is 21 and the remainder is 0.</p>
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<p><strong>Step 3</strong>- Repeat the previous step. 21 / 2 = 10. Now, the quotient is 10, and 1 is the remainder.</p>
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<p><strong>Step 3</strong>- Repeat the previous step. 21 / 2 = 10. Now, the quotient is 10, and 1 is the remainder.</p>
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<p><strong>Step 4</strong>- Repeat the previous step. 10 / 2 = 5. The quotient is 5, and the remainder is 0.</p>
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<p><strong>Step 4</strong>- Repeat the previous step. 10 / 2 = 5. The quotient is 5, and the remainder is 0.</p>
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<p><strong>Step 5</strong>- Continue the process. 5 / 2 = 2. The quotient is 2, and 1 is the remainder.</p>
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<p><strong>Step 5</strong>- Continue the process. 5 / 2 = 2. The quotient is 2, and 1 is the remainder.</p>
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<p><strong>Step 6</strong>- Continue the process. 2 / 2 = 1. The quotient is 1, and 0 is the remainder.</p>
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<p><strong>Step 6</strong>- Continue the process. 2 / 2 = 1. The quotient is 1, and 0 is the remainder.</p>
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<p><strong>Step 7</strong>- Final step. 1 / 2 = 0. 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 7</strong>- Final step. 1 / 2 = 0. 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 8</strong>- Write down the remainders from bottom to top. Therefore, 85 (decimal) = 1010101 (binary).</p>
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<p><strong>Step 8</strong>- Write down the remainders from bottom to top. Therefore, 85 (decimal) = 1010101 (binary).</p>
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