1.8 For a 32-bit two's complement signed fixed-point rep presentation with 16 integer bits and 16 fractional bits, is the distance between two neighboring numbers the same? Why?

1.4 What is the minimum magnitude of ordinary numbers (i.e, other than zero) in single precision foating-point representation? Express your answer in format of x..cx---xx× where x∈ (0,1) and e is the decimal value of the exponent.

1.5 What is the minimum magnitude of subnormal numbers in single precision floating-point represcntation? Express your answer in format of x..xx...xx× where x ∈ [0,1J and e is the decimal value of the exponent.

1.6 What is the representable range of the single-precision floating-point numbers?

1.7 Is the distance between two neighboring singlo-precision foating-point numbers the same?

1.9 Continued with the previous 32-bit signed fixed-point representation, what is the representable range of the 32-bit signed fixed-point format?

1.10 In general, addition of two 32-bit fixed-point numbers can be finished in one clock cycle. However, addition of two single-precision floating-point numbers usually takes more than one clock cycle. Why? Hint: explain using the operations involved in floating-point addition/subtraction. Why? 

2.2 If you want to achieve a speedup of 80 for a computation task using 100 processots running concurrently, what faction of the computation task can be sequential according to Amdahl's law?

2.3 For an application program running on a multi-processor system with 32 processors, it takes 200 ns to handle reference in a remote memory. Assume that this application program always bas hits in the local mem nory except for remote memor ry access involving commun nication. Proc cessors are stalled on a remote request, and the processor clock is 3.3 GHz. Assume that the base CPI (cycles per instruction) is 0.5 and all references hit in cache. How much faster is the multi-processor if there is no communicatio ion versus if 0.2% of instructions s involve remote e communication. references? Hint: compute the new CPI first. The speedup is the ratio of the two CPI values.

2.4 Assume that 25% operations of a computation task are floating-point operations and average CPI (cycles per instruction) for floating-point operations and other operations are 4.0 and 1.33 respectively. Sup ppose that 2% of the floating-poi operations in the task are floating- -point division which has CPI = 20. Assume that the two design altemnatives are to decrease the CPI of the foating- point division to 2 or the decrease the average CPI of all floating-point operations to 2.5. Compare these two design alternatives using processor performance equation. Which design choice is better? Why? Hint: compute the CPI values of different designs. e the floating-point

3.1 What is the maximun m working frequency of the above CPU?