CDA4101, Assignment 1

Due Sunday 2/8 (not late until 6 am 2/9)

1. (4 points total) Consider a three level computer and three equivalent programs for each level. Equivalent programs are written in the language of that level and do the same work. For example, one level might be a Java machine and another level might be an assembly program.

   • One level 3 instruction does three times the work of a level 2 instruction.
   • One level 2 instruction does four times the work of a level 1 instruction.

   Each level has its own hardware implementation, independent of the other levels. No interpretation is needed.

   1. (1 point) If a level 1 program takes 52 seconds to run, how long would an equivalent level 2 program run?
   2. (1 point) If a level 1 program takes 60 seconds to run, how long would an equivalent level 3 program run?

   In reality, there is only one hardware implementation. Level 3 instructions must be interpreted to Level 2 and Level 2 instructions must be interpreted to Level 1.

   • Four level 2 instruction are required to interpret a level 3 instruction.
   • Two level 1 instruction are required to interpret a level 2 instruction.

   Modify your answers from above to take into account that interpretation is being done for each level.

   3. (1 point) If a level 1 program takes 50 52 seconds to run, how long would the level 2 program run?
   4. (1 point) If a level 1 program takes 60 seconds to run, how long would the level 3 program run?
2. (2 points) Consider a three level computer.
   • It takes 4 level 2 instructions to interpret a level 3 instruction.
   • It takes 3 level 1 instructions to interpret a level 2 instruction.
   1. How many level 1 instructions would be run when interpreting a 12 instruction level 3 program?
   2. How many level 3 instructions would be in the origianl program if the level 1 equivalent program had 348 instructions?
3. (5 points) Identify the computer:
   1. First Intel computer with a single, five-stage pipeline
   2. First Intel computer with a dual, five-stage pipeline
   3. First Intel computer with a superscalar pipeline
   4. First commercial RISC machine
   5. First computer with a single bus
4. (4 points total) Consider a student record with name, age, and major number. The name is Pat Adams, the age is 19, the major number is 2022. Show how the data would be stored in a memory system that has 4-byte words as follows:
   1. (2 points) Store the data using Big Endian
   2. (2 points) Store the data using Little Endian
5. (4 points) How long does it take to read a disk with 8000 cylinders, each containing 8 tracks (4 platters) of 1024 sectors? First, read all the sectors on all the tracks in cylinder 0, then read all the sectors in all the tracks of cylinder 1, etc. The rotation time is 8 msec. A seek takes 1 msec between adjacent cylinders and 18 msec in the worst case. Switching between tracks of a cylinder is instantaeous. Show your work in discrete steps.
6. (3 points) List the maximum throughput for the following:
   1. ATAPI-6
   2. ATAPI-7
   3. Wide Ultra SCSI
7. (2 points) Research RAID6 on the web
   1. Explain how RAID6 is implemented differently from RAID5.
   2. How many drives can RAID6 lose?
8. (2 points) Suppose a device can read 16MB/sec and has a capacity of 60GB. How minutes does it take to read the entire device?
9. (2 points) A bit-map terminal has a 2500x2000 display. The display is redrawn 50 times a second. How many nanoseconds is the pulse corresponding to one pixel?
10. (2 points) Prove whether or not these equations are equivalent by using truth tables. Do not simplify the expressions.
    • A + BC
    • (A + B)(A + C)
11. (3 points total) Consider the three input boolean function that is a 1 if the binary equivalent of the inputs is 0, 2, 3, 5, 7.
    • (2) Draw a circuit diagram for this function using only 2-input NOR gates.
    • (1) Draw a circuit diagram for this function using the MSI multiplexer chip in the Multiplexers section of the book. Do not draw the inside of the multiplexer.
12. (3 points total) A 2-bit encoder is a circuit with four input lines, exactly one of which is high at every instant, and two output lines whose 2-bit binary value tells which input is high. Only one of the input lines will ever be active at the same time. You do not have to consider the cases if more than one is active.
    1. (1) Draw the truth table for a 2-bit encoder. There will be four input variables and two output variables. Only one of the input variables can be 1 at a given time, so there are only 4 possible combinations for valid input variables.
    2. (1) Draw the circuit for the 2-bit encoder.
    3. (1) Draw the circuit for a 3-bit encoder. There will be 8 input lines and 3 output lines.
       
13. (4 points) The shifter from the book only has two functions: logical shift right and logical shift left. Create a new circuit that implements a 4-bit shifter with four functions: arithmetic shift right, don't shift, logical shift left, logical shift right. The shifting done in the book is logical shifting: a 0 is placed into the S0 or S7 bit, depending on which way the shift goes. An arithmetic shift right places D0 into both S0 and S1: it is duplicating the sign bit. A don't shift operation would send each data bit to the corresponding output: D0 to S0, D1 to S1, etc. Be sure that only one of these functions is enabled at a time.
    

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