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Original
2026-01-01
Modified
2026-02-28
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<p>1989 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>1989 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><strong>Expansion Method:</strong>Let us see the step-by-step process of converting 1989 using the expansion method.</p>
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<p><strong>Expansion Method:</strong>Let us see the step-by-step process of converting 1989 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>211 = 2048</p>
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<p>211 = 2048</p>
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<p>Since 2048 is<a>greater than</a>1989, we stop at 210 = 1024.</p>
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<p>Since 2048 is<a>greater than</a>1989, we stop at 210 = 1024.</p>
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<p><strong>Step 2 -</strong>Identify the largest power of 2: In the previous step, we stopped at 210 = 1024. 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, 1989. Since 210 is the number we are looking for, write 1 in the 210 place. Now the value of 210, which is 1024, is subtracted from 1989. 1989 - 1024 = 965.</p>
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<p><strong>Step 2 -</strong>Identify the largest power of 2: In the previous step, we stopped at 210 = 1024. 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, 1989. Since 210 is the number we are looking for, write 1 in the 210 place. Now the value of 210, which is 1024, is subtracted from 1989. 1989 - 1024 = 965.</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, 965. So, the next largest power of 2 is 29, which is less than or equal to 965. Now, we have to write 1 in the 29 place. And then subtract 512 from 965. 965 - 512 = 453.</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, 965. So, the next largest power of 2 is 29, which is less than or equal to 965. Now, we have to write 1 in the 29 place. And then subtract 512 from 965. 965 - 512 = 453.</p>
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<p><strong>Step 4 -</strong>Repeat until remainder is 0: Continue identifying the next largest power of 2 and writing 1 in those places. Subtract until the remainder is 0.</p>
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<p><strong>Step 4 -</strong>Repeat until remainder is 0: Continue identifying the next largest power of 2 and writing 1 in those places. Subtract until the remainder is 0.</p>
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<p><strong>Step 5 -</strong>Fill in with 0s: For unused place values, write 0. Now, by substituting the values, we get the binary representation of 1989 as 11111000101.</p>
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<p><strong>Step 5 -</strong>Fill in with 0s: For unused place values, write 0. Now, by substituting the values, we get the binary representation of 1989 as 11111000101.</p>
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<p><strong>Grouping Method:</strong>In this method, we divide the number 1989 by 2. Let us see the step-by-step conversion.</p>
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<p><strong>Grouping Method:</strong>In this method, we divide the number 1989 by 2. Let us see the step-by-step conversion.</p>
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<p><strong>Step 1 -</strong>Divide the given number 1989 by 2. 1989 / 2 = 994. Here, 994 is the quotient and 1 is the remainder.</p>
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<p><strong>Step 1 -</strong>Divide the given number 1989 by 2. 1989 / 2 = 994. Here, 994 is the quotient and 1 is the remainder.</p>
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<p><strong>Step 2 -</strong>Divide the previous quotient (994) by 2. 994 / 2 = 497. Here, the quotient is 497 and the remainder is 0.</p>
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<p><strong>Step 2 -</strong>Divide the previous quotient (994) by 2. 994 / 2 = 497. Here, the quotient is 497 and the remainder is 0.</p>
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<p><strong>Step 3 -</strong>Repeat the previous step. 497 / 2 = 248. Now, the quotient is 248, and 1 is the remainder.</p>
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<p><strong>Step 3 -</strong>Repeat the previous step. 497 / 2 = 248. Now, the quotient is 248, and 1 is the remainder.</p>
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<p><strong>Step 4 -</strong>Continue dividing until the quotient is 0.</p>
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<p><strong>Step 4 -</strong>Continue dividing until the quotient is 0.</p>
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<p><strong>Step 5 -</strong>Write down the remainders from bottom to top. Therefore, 1989 (decimal) = 11111000101 (binary).</p>
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<p><strong>Step 5 -</strong>Write down the remainders from bottom to top. Therefore, 1989 (decimal) = 11111000101 (binary).</p>
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