Fill in the boxes to show how the value 4.75 can be represented in binary scientific notation:
Question
Fill in the boxes to show how the value 4.75 can be represented in binary scientific notation:
Solution
Binary scientific notation represents numbers as a binary decimal and an exponent of two.
Here's how to convert 4.75 into binary scientific notation:
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Convert the whole number part (4) to binary: 4 in binary is 100.
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Convert the decimal part (0.75) to binary: 0.75 in binary is 0.11.
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Combine the two parts: 4.75 in binary is 100.11.
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Normalize the binary number: Move the binary point two places to the left to get 1.0011. This is the mantissa.
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The exponent is the number of places you moved the binary point. Since we moved it two places to the right, the exponent is 2.
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Write the exponent in binary: 2 in binary is 10.
So, 4.75 in binary scientific notation is 1.0011 x 2^10.
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