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For the following question, we will be following the IEEE-754 Floating Point standard but with different numbers of bits: with 6 bits of exponent, an
For the following question, we will be following the IEEE-754 Floating Point standard but with different numbers of bits: with 6 bits of exponent, an exponent bias of 31, and 25 bits of mantissa. Due to PrairieLearn restrictions, please submit your answer as the full number. Floating point representations present a trade-off between range and accuracy. Due to the limited significant digits that you can represent, there will be a point where integers cannot be exactly represented anymore. Q1.1: What's the smallest non-infinite positive integer (whole number) this representation CANNOT represent? Hint: When the step size becomes 2, you start skipping whole numbers. The floating point standard optimizes the representation of numbers by not including the implied 1 for the 'normal' binary representations. Q1.2: What power of 2 is the smallest representable positive normalized number? Submit the exponent only. Floating point also allows for representations of numbers even smaller than the smallest normalized number. Denormal numbers utilize an implied 0 , instead of an implied 1. Q1.3: What power of 2 is the smallest representable positive value? Submit the exponent only. Q1.4: How many NaNs can be represented with this floating point system? Hint: Recall how NaNs are represented following the floating point standard. Q1.5: What's the most negative possible denormalized number representable in this system? Write the value in IEEE-754 hexadecimal notation (with uppercase letters), including the "0x" prefix
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