CDA4101, Assignment 1

Due Friday 9/26 (not late until 6 am 9/27)

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 two times the work of a level 2 instruction.
   • Three level 2 instruction are required to interpret a level 3 instruction.
   • One level 2 instruction does five times the work of a level 1 instruction.
   • Three level 1 instruction are required to interpret a level 2 instruction.
   1. (2 points) If a level 1 program takes 50 seconds to run, how long would an equivalent level 2 program run?
   2. (2 points) If a level 1 program takes 60 seconds to run, how long would an equivalent level 3 program run?
2. (2 points) Consider a three level computer.
   • It takes 5 level 2 instructions to interpret a level 3 instruction.
   • It takes 4 level 1 instructions to interpret a level 2 instruction.
   • How many level 1 instructions would be run when interpreting a 10 instruction level 3 program?
3. (2 points) Suppose a device can read 32MB/sec and has a capacity of 30GB. How minutes does it take to read the entire device?
4. (2 points) A bit-map terminal has a 1666x1000 display. The display is redrawn 75 times a second. How many nanoseconds is the pulse corresponding to one pixel?
5. (2 points) Prove whether or not these equations are equivalent by using truth tables. Do not simplify the expressions. (! is NOT).
   • !ABC + AB!C + A!B!C + !A!BC
   • A XOR C. Add a column to the above truth table and calculate XOR for the A and C columns, even though some values are repeated.
6. (3 points total) Consider the three input boolean function that is a 1 if the binary equivalent of the inputs is 1, 2, 3, 4, 7.
   • (2) Draw a circuit diagram for this function using only NOR gates.
   • (1) Draw a circuit diagram for this function using the MSI multiplexer chip in the Multiplexers section of the book.
7. (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.
      
8. (3 points) Using the MSI Multiplexer chip in the Multiplexers section of the book and one inverter, implement the 4-input boolean function that is a 1 when the binary equivalent of the inputs is 1, 2, 7, 9, 12, 14, or 15 . Label the 4 inputs as A, B, C, and D. (Hint: Vcc, Ground, D, not D). You may use an additional inverter and additional AND gates. You must use the multiplexer as it is shown: it has only three input lines, A, B, C.
   
9. (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.
   

Submitting the Assignment

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Course Objectives met by this Homework