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Using a normalised floating point representation box with an 8-bit mantissa and a 4-bit exponent, both stored using two’s complement.

(a) Write the smallest positive number that can be represented by the floating point system in the boxes below. The result is: Mantissa 0.1000000 and exponent 1000

Do not see how this can could someone please explain.

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  • $\begingroup$ We're not looking for posts that simply copy the text of an exercise-style task and ask us to solve it for you. You might find this page helpful in improving your question. Make sure to credit the original source of all copied material. $\endgroup$ – D.W. Feb 23 at 3:37
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It is 0.100000, because normalised values are only allowed to start with 01 or 10. The exponent is 1000 (-8 in decimal) because that is the smallest possible value that can be represented using two's compliment in 4 bits. The value of the exponent means that the floating point will be moved 8 values to the left, thus making the result smaller.

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That depends on the exact details of the floating point representation. Several are possible. Much more detail than you ever wanted to know is available here.

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