Chapter 3: 42 (page 241)
What do you get if you add to itself 4 times? What is ? Are they the same? What should they be?
The value of adding –1/4 four times and the value of multiplying –1/4 by 4 are the same.
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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.
[30] <§3.5> If the bit pattern 0×0C000000 is placed into the Instruction Register, what MIPS instruction will be executed?
Question : 3.28 [20] The Hewlett-Packard 2114, 2115, and 2116 used a format with the left most 16 bits being the fraction stored in two’s complement format, followed by another 16-bit field which had the left most 8 bits as an extension of the fraction (making the fraction 24 bits long), and the rightmost 8 bits representing the exponent. However, in an interesting twist, the exponent was stored in sign-magnitude format with the sign bit on the far right! Write down the bit pattern to represent 
assuming this format. No hidden 1 is used. Comment on how the range and accuracy of this 32-bit pattern compares to the single precision IEEE 754 standards.
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.
As discussed in the text, one possible performance enhancement is to do a shift and add instead of actual multiplication. Since , for example, can be written , we can calculate by shifting 6 to the left 3 times and then adding 6 to that result. Show the best way to calculate using shifts and adds/subtracts. Assume both inputs are 8 bit unsigned integers.
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