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Original
2026-01-01
Modified
2026-02-28
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<p>1023 can be easily converted from decimal to binary. Below are methods to help convert the number. Let’s see how it is done.</p>
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<p>1023 can be easily converted from decimal to binary. Below are methods to help 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 1023 using the expansion method.</p>
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<p>Expansion Method: Let us see the step-by-step process of converting 1023 using the expansion method.</p>
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<p>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 identify the powers of 2. 2^0 = 1 2^1 = 2 2^2 = 4 2^3 = 8 ... 2^9 = 512 2^10 = 1024 Since 1024 is<a>greater than</a>1023, we stop at 2^9 = 512.</p>
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<p>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 identify the powers of 2. 2^0 = 1 2^1 = 2 2^2 = 4 2^3 = 8 ... 2^9 = 512 2^10 = 1024 Since 1024 is<a>greater than</a>1023, we stop at 2^9 = 512.</p>
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<p>Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2^9 = 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, 1023. Since 2^9 is the number we are looking for, we write 1 in the 2^9 place. Now the value of 2^9, which is 512, is subtracted from 1023. 1023 - 512 = 511.</p>
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<p>Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2^9 = 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, 1023. Since 2^9 is the number we are looking for, we write 1 in the 2^9 place. Now the value of 2^9, which is 512, is subtracted from 1023. 1023 - 512 = 511.</p>
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<p>Step 3 - Continue this process: 511 - 256 = 255 255 - 128 = 127 127 - 64 = 63 63 - 32 = 31 31 - 16 = 15 15 - 8 = 7 7 - 4 = 3 3 - 2 = 1 1 - 1 = 0 The binary representation is 1111111111.</p>
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<p>Step 3 - Continue this process: 511 - 256 = 255 255 - 128 = 127 127 - 64 = 63 63 - 32 = 31 31 - 16 = 15 15 - 8 = 7 7 - 4 = 3 3 - 2 = 1 1 - 1 = 0 The binary representation is 1111111111.</p>
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<p>Grouping Method: In this method, we divide the number 1023 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 1023 by 2. Let us see the step-by-step conversion.</p>
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<p>Step 1 - Divide the given number 1023 by 2. 1023 / 2 = 511,<a>remainder</a>1. Continue dividing the quotient: 511 / 2 = 255, remainder 1. 255 / 2 = 127, remainder 1. 127 / 2 = 63, remainder 1. 63 / 2 = 31, remainder 1. 31 / 2 = 15, remainder 1. 15 / 2 = 7, remainder 1. 7 / 2 = 3, remainder 1. 3 / 2 = 1, remainder 1. 1 / 2 = 0, remainder 1. Step 5 - Write down the remainders from bottom to top. Therefore, 1023 (decimal) = 1111111111 (binary).</p>
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<p>Step 1 - Divide the given number 1023 by 2. 1023 / 2 = 511,<a>remainder</a>1. Continue dividing the quotient: 511 / 2 = 255, remainder 1. 255 / 2 = 127, remainder 1. 127 / 2 = 63, remainder 1. 63 / 2 = 31, remainder 1. 31 / 2 = 15, remainder 1. 15 / 2 = 7, remainder 1. 7 / 2 = 3, remainder 1. 3 / 2 = 1, remainder 1. 1 / 2 = 0, remainder 1. Step 5 - Write down the remainders from bottom to top. Therefore, 1023 (decimal) = 1111111111 (binary).</p>
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