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Original
2026-01-01
Modified
2026-02-28
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<p>480 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>480 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 480 using the expansion method.</p>
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<p>Expansion Method: Let us see the step-by-step process of converting 480 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 Since 256 is the largest power of 2<a>less than</a>480, we begin with 2^8.</p>
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<p>28 = 256 Since 256 is the largest power of 2<a>less than</a>480, we begin with 2^8.</p>
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<p><strong>Step 2</strong>- Identify the largest power of 2: In the previous step, we stopped at 28 = 256. This is because in this step, we have to identify the largest power of 2, which is less than or equal to the given number, 480. Since 28 is the number we are looking for, write 1 in the 28 place. Now the value of 28, which is 256, is subtracted from 480. 480 - 256 = 224.</p>
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<p><strong>Step 2</strong>- Identify the largest power of 2: In the previous step, we stopped at 28 = 256. This is because in this step, we have to identify the largest power of 2, which is less than or equal to the given number, 480. Since 28 is the number we are looking for, write 1 in the 28 place. Now the value of 28, which is 256, is subtracted from 480. 480 - 256 = 224.</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, 224. So, the next largest power of 2 is 27, which is 128. Now, we have to write 1 in the 27 place. And then subtract 128 from 224. 224 - 128 = 96.</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, 224. So, the next largest power of 2 is 27, which is 128. Now, we have to write 1 in the 27 place. And then subtract 128 from 224. 224 - 128 = 96.</p>
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<p><strong>Step 4</strong>- Continue the process: Identify the largest power of 2 that fits into 96. It is 26 = 64. Write 1 in the 26 place and subtract 64 from 96. 96 - 64 = 32. Now, 32 fits perfectly into 25, so write 1 in the 25 place and subtract. 32 - 32 = 0.</p>
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<p><strong>Step 4</strong>- Continue the process: Identify the largest power of 2 that fits into 96. It is 26 = 64. Write 1 in the 26 place and subtract 64 from 96. 96 - 64 = 32. Now, 32 fits perfectly into 25, so write 1 in the 25 place and subtract. 32 - 32 = 0.</p>
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<p><strong>Step 5</strong>- Identify the unused place values: In previous steps, we wrote 1 in the 28, 27, 26, and 25 places. Now, we can just write 0s in the remaining places, which are 24, 23, 22, 21, and 20. Now, by substituting the values, we get: 0 in the 20 place 0 in the 21 place 0 in the 22 place 0 in the 23 place 0 in the 24 place 1 in the 25 place 1 in the 26 place 1 in the 27 place 1 in the 28 place Therefore, the binary representation of 480 is 111100000.</p>
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<p><strong>Step 5</strong>- Identify the unused place values: In previous steps, we wrote 1 in the 28, 27, 26, and 25 places. Now, we can just write 0s in the remaining places, which are 24, 23, 22, 21, and 20. Now, by substituting the values, we get: 0 in the 20 place 0 in the 21 place 0 in the 22 place 0 in the 23 place 0 in the 24 place 1 in the 25 place 1 in the 26 place 1 in the 27 place 1 in the 28 place Therefore, the binary representation of 480 is 111100000.</p>
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<p>Grouping Method: In this method, we divide the number 480 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 480 by 2. Let us see the step-by-step conversion.</p>
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<p><strong>Step 1</strong>- Divide the given number 480 by 2. 480 / 2 = 240. Here, 240 is the quotient and 0 is the remainder.</p>
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<p><strong>Step 1</strong>- Divide the given number 480 by 2. 480 / 2 = 240. Here, 240 is the quotient and 0 is the remainder.</p>
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<p><strong>Step 2</strong>- Divide the previous quotient (240) by 2. 240 / 2 = 120. Here, the quotient is 120 and the remainder is 0.</p>
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<p><strong>Step 2</strong>- Divide the previous quotient (240) by 2. 240 / 2 = 120. Here, the quotient is 120 and the remainder is 0.</p>
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<p><strong>Step 3</strong>- Repeat the previous step. 120 / 2 = 60. Now, the quotient is 60, and 0 is the remainder.</p>
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<p><strong>Step 3</strong>- Repeat the previous step. 120 / 2 = 60. Now, the quotient is 60, and 0 is the remainder.</p>
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<p><strong>Step 4</strong>- Continue the<a>division</a>process. 60 / 2 = 30, remainder 0. 30 / 2 = 15, remainder 0. 15 / 2 = 7, remainder 1. 7 / 2 = 3, remainder 1. 3 / 2 = 1, remainder 1. 1 / 2 = 0, remainder 1. Write down the remainders from bottom to top. Therefore, 480 (decimal) = 111100000 (binary).</p>
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<p><strong>Step 4</strong>- Continue the<a>division</a>process. 60 / 2 = 30, remainder 0. 30 / 2 = 15, remainder 0. 15 / 2 = 7, remainder 1. 7 / 2 = 3, remainder 1. 3 / 2 = 1, remainder 1. 1 / 2 = 0, remainder 1. Write down the remainders from bottom to top. Therefore, 480 (decimal) = 111100000 (binary).</p>
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