# PROBLEMS. which was discussed in Section

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1 22 CHAPTER 1 BASIC STRUCTURE OF COMPUTERS (Corrisponde al cap. 1 - Introduzione al calcolatore) PROBLEMS 1.1 List the steps needed to execute the machine instruction LOCA,R0 in terms of transfers between the components shown in Figure 1.2 and some simple control commands. Assume that the instruction itself is stored in the memory at location INSTR and that this address is initially in register PC. The first two steps might be expressed as Transfer the contents of register PC to register MAR. Issue a Read command to the memory, and then wait until it has transferred the requested word into register MDR. Remember to include the steps needed to update the contents of PC from INSTR to INSTR+1 so that the next instruction can be fetched. 1.2 Repeat Problem 1.1 for the machine instruction R1,R2,R3 which was discussed in Section (a) Give a short sequence of machine instructions for the task: the contents of memory location A to those of location B, and place the answer in location C. Instructions LOC,R i and Store R i,loc are the only instructions available to transfer data between the memory and generalpurpose register R i. instructions were described in Sections 1.3 and Do not destroy the contents of either location A or B. (b) Suppose that Move and instructions are available with the format Move/ Location1,Location2 These instructions move or add a copy of the operand at the first location to the second location, overwriting the original operand at the second location. Locationi can be in either the memory or the processor register set. Is it possible to use fewer instructions to accomplish the task in Part a? If yes, give the sequence. 1.4 (a) Section 1.5 discusses how the input and output steps of a collection of programs such as the one shown in Figure 1.4 could be overlapped to reduce the total time needed to execute them. Let each of the six OS routine execution intervals be 1 unit of time, with each disk operation requiring 3 units, printing requiring 3 units, and each program execution interval requiring 2 units of time. Compute the ratio of

2 best overlapped time to nonoverlapped time for a long sequence of programs. Ignore start-up and ending transients. (b) Section 1.5 indicated that program computation can be overlapped with either input or output operations or both. Ignoring the relatively short time needed for OS routines, what is the ratio of best overlapped time to nonoverlapped time for completing the execution of a collection of programs, where each program has about equal balance among input, compute, and output activities? 1.5 (a) Program execution time, T,asdefined in Section 1.6.2, is to be examined for a certain high-level language program. The program can be run on a RISC or a CISC computer. Both computers use pipelined instruction execution, but pipelining in the RISC machine is more effective than in the CISC machine. Specifically, the effective value of S in the T expression for the RISC machine is 1.2, but it is only 1.5 for the CISC machine. Both machines have the same clock rate, R. What is the largest allowable value for N, the number of instructions executed on the CISC machine, expressed as a percentage of the N value for the RISC machine, if time for execution on the CISC machine is to be no longer than that on the RISC machine? (b) Repeat Part a if the clock rate, R, for the RISC machine is 15 percent higher than that for the CISC machine. 1.6 (a) A processor cache, as shown in Figure 1.5, is discussed in Section 1.6. Suppose that execution time for a program is directly proportional to instruction access time and that access to an instruction in the cache is 20 times faster than access to an instruction in the main memory. Assume that a requested instruction is found in the cache with probability 0.96, and also assume that if an instruction is not found in the cache, it must first be fetched from the main memory to the cache and then fetched from the cache to be executed. Compute the ratio of program execution time without the cache to program execution time with the cache. This ratio is usually defined as the speedup factor resulting from the presence of the cache. (b) If the size of the cache is doubled, assume that the probability of not finding a requested instruction there is cut in half. Repeat Part a for a doubled cache size.

3 SOLUTIONS - Chapter 1 Basic Structure of Computers 1.1. Transfer the contents of register PC to register MAR Issue a Read command to memory, and then wait until it has transferred the requested word into register MDR Transfer the instruction from MDR into IR and decode it Transfer the address LOCA from IR to MAR Issue a Read command and wait until MDR is loaded Transfer contents of MDR to the ALU Transfer contents of R0 to the ALU Perform addition of the two operands in the ALU and transfer result into R0 Transfer contents of PC to ALU 1 to operand in ALU and transfer incremented address to PC 1.2. First three steps are the same as in Problem (a) Transfer contents of R1 and R2 to the ALU Perform addition of two operands in the ALU and transfer answer into R3 Last two steps are the same as in Problem 1.1 (b) Yes; Store A,R0 B,R1 R0,R1 R1,C Move B,C A,C 1.4. (a) Non-overlapped time for Program i is 19 time units composed as: Program i input compute output 1

4 Overlapped time is composed as: Program i output 1 15 time units Program i input compute output Program i input Time between successive program completions in the overlapped case is 15 time units, while in the non-overlapped case it is 19 time units. Therefore, the ratio is 15/19. (b) In the discussion in Section 1.5, the overlap was only between input and output of two successive tasks. If it is possible to do output from job i 1, compute for job i, and input to job i+1 at the same time, involving all three units of printer, processor, and disk continuously, then potentially the ratio could be reduced toward 1/3. The OS routines needed to coordinate multiple unit activity cannot be fully overlapped with other activity because they use the processor. Therefore, the ratio cannot actually be reduced to 1/ (a) Let T R = (N R S R ) / R R and T C = (N C S C ) / R C be execution times on the RISC and CISC processors, respectively. Equating execution times and clock rates, we have Then 1.2 N R = 1.5 N C N C / N R = 1.2 / 1.5 = 0.8 Therefore, the largest allowable value for N C is 80% of N R. 2

5 (b) In this case 1.2 N R / 1.15 = 1.5 N C / 1.00 Then N C / N R = 1.2 / ( ) = Therefore, the largest allowable value for N C is 69.6% of N R (a) Let cache access time be 1 and main memory access time be 20. Every instruction that is executed must be fetched from the cache, and an additional fetch from the main memory must be performed for 4% of these cache accesses. Therefore, (b) Speedup factor = Speedup factor = (1.0 1) + ( ) = (1.0 1) + ( ) =

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