CDA4101, Assignment 1

Due Monday 9/21

1. 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?
2. 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 bus for I/O
3. 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. Store the data using Big Endian
   2. Store the data using Little Endian
4. Prove whether or not these equations are equivalent by using truth tables. Do not simplify the expressions.
   • A(B + C)
   • AB + BC
5. Consider the three input boolean function that is a 1 if the binary equivalent of the inputs is 0, 1, 3, 6, 7.
   • Draw a circuit diagram for this function using only 2-input NOR gates.
   • 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.
6. 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. 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. Draw the circuit for the 2-bit encoder.
   3. Draw the circuit for a 3-bit encoder. There will be 8 input lines and 3 output lines.
      
7. A 2-bit demultiplexer is a circuit with one input line, two control lines and four output lines. The input line will appear on one of the output lines based on the control lines. Draw the circuit for a 2-bit demultiplexer.
8. 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.
9. The book shows how to create an adder from two half-adders. A subtractor can be created in a similar fashion.
   1. Draw the truth table for a half-subtractor.
   2. Draw the circuit for a half-subtractor.
   3. Draw the truth table for a full subtractor.
   4. Draw the circuit for a full subtractor.
10. List the control signals for the ALU to generate the following:
    1. A OR B
    2. The constant 1
    3. The constant -1
    4. B - A

Quiz

The quiz for this assignment will be on Wednesday, September 23 Monday, September 28. We will review the solution to this assignment in class on Monday, September 21.