Chapter 3: 15 (page 238)
Calculate the time necessary to perform a multiply using the approach described in the text (31 adders vertically) if an integer is 8 bits wide and an adder takes 4 time units.
Time units that is necessary to perform a multiplication:
28 time units
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Write down the binary representation of the decimal number 63.25 assuming it was stored using the single precision IBM format (base 16, instead of base 2, with 7 bits of exponent).
Question: Write down the bit pattern in the fraction assuming a floating-point format that uses Binary Coded Decimal (base 10) numbers in the fraction instead of base 2. Assume there are 24 bits, and you do not need to normalize. Is this representation exact?
IEEE 754-2008 contains a half precision that is only 16 bits wide. The left most bit is still the sign bit, the exponent is 5 bits wide and has a bias of 15, and the mantissa is 10 bits long. A hidden 1 is assumed. Write down the bit pattern to represent assuming a version of this format, which uses an excess-16 format to store the exponent. Comment on how the range and accuracy of this 16-bit floating point format compares to the single precision IEEE 754 standard.
Assume 151 and 214 are signed 8-bit decimal integers stored in two’s complement format. Calculate using saturating arithmetic. The result should be in decimal. Show your work.
Calculate by hand, assuming each of the values are stored in the 16-bit half precision format described in Exercise 3.27 ( and also described in the text). Assume 1 guard, 1 round bit, and 1 sticky bit, and round to the nearest even. Show all the steps, and write your answer in both the 16-bit floating point format and in decimal.
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