Engineering, 06.05.2020 01:44 kels7618

Suppose you have a binary, 16-bit, normalized floating-point number system, with 1 bit for the sign, 5 bits for the exponent, and the remaining 10 bits for the fraction. Since there are 5 bits for the exponent, there are 32 possible values, making the range -15 to 16, therefore the bias is 15. As always, the lowest exponent, -15 (stored as all zeroes) is reserved for representing zero and denormalized numbers, so the lowest normalized exponent is -14 (which is also the effective exponent for denormalized numbers). The largest exponent, 16 (stored as all ones), is reserved for NaNs and infinities, so the largest normalized exponent is 15. Answer the following questions about the number system above. (4 points each) 2. What is the precision, p? a) b) What is the spacing between floating-point numbers in the range [4,8]? c) How would the number 6.5 be represented in this number system? d) What number is represented by the following 16 bits in this number system. 1100110110100000

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Suppose you have a binary, 16-bit, normalized floating-point number system, with 1 bit for the sign,...

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