-8 is equal to signed binary number *(A) 10001000(B )10000000(C) 00001000(D) 11000000
Question
-8 is equal to signed binary number *(A) 10001000(B )10000000(C) 00001000(D) 11000000
Solution
The answer is (B) 10000000.
Here's the step-by-step process:
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First, we need to understand that binary numbers can be represented in signed magnitude, where the leftmost bit is used to represent the sign of the number (0 for positive, 1 for negative), and the remaining bits represent the magnitude of the number.
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In this case, we are looking for the binary representation of -8.
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The binary representation of 8 (ignoring the sign for now) is 1000.
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Since we are looking for -8, we need to represent this as a negative number in signed magnitude. This means we put a 1 at the front of the binary number to represent the negative sign.
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However, we need to make sure the binary number has 8 bits (as per the options given). So, we pad the number with zeros at the front, giving us 00001000.
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Finally, we add the sign bit at the front, giving us 10000000.
So, the signed binary representation of -8 is 10000000, which corresponds to option (B).
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