Chapter 3: 6 (page 237)
Assume 185 and 122 are unsigned 8-bit decimal integers. Calculate 185 – 122. Is there overflow, underflow, or neither?
63,Neither
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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.
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.
Using a table similar to that shown in Figure 3.6, calculate the product of the octal unsigned 6-bit integers 62 and 12 using the hardware described in Figure 3.3. You should show the contents of each register on each step.
The following C code implements a four-tap FIR filter on input array sig_in. Assume that all arrays are 16-bit fixed-point values. for (i 3;i< 128;i ) sig_out[i] sig_in[i-3] * f[0] sig_in[i-2] * f[1] sig_in[i-1] * f[2] sig_in[i] * f[3]; Assume you are to write an optimized implementation this code in assembly language on a processor that has SIMD instructions and 128-bit registers. Without knowing the details of the instruction set, briefly describe how you would implement this code, maximizing the use of sub-word operations and minimizing the amount of data that is transferred between registers and memory. State all your assumptions about the instructions you use.
What is when these values represent unsigned 12-bit octal numbers? The result should be written in octal. Show your work.
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