(b) Color your graph using as few colors as you can. Call the computers registersR1, R2, etc. Describe the assignment of variables to registers implied by yourcoloring. How many registers do you need?(c) Suppose that a variable is assigned a value more than once, as in the codesnippet below:t =r + su = t * 3t =mkV = t + uHow might you cope with this complication? 4. A portion of a computer program consists of a sequence of calculations where theresults are stored in variables, like this (with inputs a, b and outputs d, g, h):Step Calculation1C = a + bd = a * Ce = c + 34f = Ceg = a + f6 h = f + 1A computer can perform such calculations most quickly if the value of each variable isstored in a register, a chunk of very fast memory inside the microprocessor. Compilersface the problem of assigning each variable in a program to a register. Computersusually have few registers, however, so they must be used wisely and reused often.This is called the register allocation problem.In the example above, variables a and b must be assigned different registers, becausethey hold distinct input values. Furthermore, c and d must be assigned differentregisters; if they used the same one, then the value of c would be overwritten in thesecond step and wed get the wrong answer in the third step. On the other hand,variables b and d may use the same register; after the first step, we no longer need band can overwrite the register that holds its value. Also, f and h may use the sameregister; once f+1 is evaluated in the last step, the register holding the value of fcan be overwritten.(a) Recast the register allocation problem as a question about graph coloring. Whatdo the vertices correspond to? Under what conditions should there be an edgebetween two vertices? Construct the graph corresponding to the example above.

(b) Color your graph using as few colors as you can. Call the computers registers R1, R2, etc. Describe the assignment of variables to registers implied by your coloring. How many registers do you need? (c) Suppose that a variable is assigned a value more than once, as in the code snippet below: t = r + S u = t * 3 t = m k v = t + u ... How might you cope with this complication?

(b) Color your graph using as few colors as you can. Call the computers registers R1, R2, etc. Describe the assignment of variables to registers implied by your coloring. How many registers do you need? (c) Suppose that a variable is assigned a value more than once, as in the code snippet below: t = r + S u = t * 3 t = m k v = t + u ... How might you cope with this complication?

Systems Architecture

7th Edition

ISBN:9781305080195

Author:Stephen D. Burd

Publisher:Stephen D. Burd

Chapter4: Processor Technology And Architecture

Section: Chapter Questions

Problem 2PE: If a microprocessor has a cycle time of 0.5 nanoseconds, what’s the processor clock rate? If the...

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If a microprocessor has a cycle time of 0.5 nanoseconds, what’s the processor clock rate? If the fetch cycle is 40% of the processor cycle time, what memory access speed is required to implement load operations with zero wait states and load operations with two wait states?
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Suppose a program segment consists of a purely sequential part which takes 100 cycles to execute, and an iterated loop which takes 400 cycles per iteration. Assume that the loop is dependent on the sequential part, i.e., both parts cannot run in parallel. Also assume that the loop iterations are independent, and cannot be further parallelized. If the loop is to be executed 100 times, what is the maximum speedup possible using an infinite number of processors (as many processors as you could possibly need) compared to a single processor?
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In a microprocessor-based system with several tasks that are supposed to be executed more or less simultaneously, there is a necessary condition for the sum of the computing times of the tasks. Please state this.
Assume that the operation times of one add instruction for the major functional units are 325 ps for memory access, 185 ps for ALU operations and 125 ps for register file read/writes. Please fill the table first and perform the following a )What is the total cycle in single-cycle implementation? b )What is the total cycle in pipelining implementation? c) What is the total cycle in pipelining implementation if there are 5 million add instructions? d) What is the total cycle in pipelining implementation for 5 million add instructions, if the stages are balanced? e)What is the speed up of pipelining implementation over single-cycle implementation?
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