17. Show how floating-point value 12.5 would be stored using IEEE-754 single precision (be sure to indicate the sign bit, the exponent, and the significand fields):
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17. Show how floating-point value 12.5 would be stored using IEEE-754 single precision (be sure
to indicate the sign bit, the exponent, and the significand fields):
18. If the floating-point number representation on a certain system has a sign bit, a 3-bit
exponent and a 4-bit significand:
a) What is the largest positive and the smallest positive number that can be stored on this?
system if the storage is normalized? (Assume no bits are implied, there is no biasing,
exponents use two's complement notation, and exponents of all zeros and all ones are
allowed.)
b) What bias should be used in the exponent if we prefer all exponents to be non-negative?
c) Why would you choose this bias?
19. Assume we are using the simple model for floating-point representation as given in this book
(the representation uses a 14-bit format, 5 bits for the exponent with a bias of 15, a normalized
mantissa of 8 bits, and a single sign bit for the number):
a) Show how the computer would represent the numbers 100.0 and 0.25 using this floating-point format.
b) Show how the computer would add the two floating-point numbers in part a by changing
one of the numbers so they are both expressed using the same power of 2.
c) Show how the computer would represent the sum in part b using the given floating-point
representation. What decimal value for the sum is the computer actually storing? Explain.
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