Fall 1997, Assignment 1

Due 9/17 at the start of class

  1. Are these two circuits equivalent? Draw the truth tables for each to prove your answer.
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  2. Consider the three input boolean function that is 1 if an odd number of input lines are 1, and 0 if an even number of input lines are 1. Draw a circuit diagram for this function:
    1. Using SSI chips listed on page 89 of the book.
    2. Using the MSI multiplexer chip.
  3. Consider the three input boolean function that is a 1 if one of the inputs is 1, and 0 if two or more of the inputs are 1. It is also 0 if all the inputs are 0.
    1. Using SSI chips listed on page 89 of the book.
    2. Using the MSI multiplexer chip.
  4. Redo questions 2 and 3, but implement both circuits on the same LSI PLA. Label the inputs for each differently (eg: A, B, C and D, E, F).Only draw the gates and lines that you use. Draw all the lines into each gate. Indicate which fuses have been blown, and which have not.
  5. A 2-bit demultiplexer is a circuit whose single input line is steered to one of the four output lines depending on the state of the two control lines.
    1. Draw the truth table for a 2-bit demultiplexer. There will be one input variable, two control variables (also input variables), and 4 output variables.
    2. Draw the circuit for a 2-bit demultiplexer.
    3. Draw the circuit for a 3-bit demultiplexer. There will be one input line, three control lines, and 8 output lines.
  6. A 2-bit encoder is a circuit with four input lines, exactly one of which is high at any instant, and two output lines whose 2-bit binary value tells which input is high.
    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 varaibles can be 1 at a given time, so there are only 4 possible states for the input variables.
    2. Draw the circuit for a 2-bit encoder.
    3. Draw the circuit for a 3-bit encoder. There will be 8 input lines and 3 output lines.
  7. Draw the truth table and try to summarize succinctly what this circuit does. Hint: it is equivalent to a circuit we covered in class.
    Look at page 157 of the text, example 12 for this image.
  8. (Page 158, #16) A 16-bit ALU is built up of 16 1-bit ALUs, each one having an add time of 100 nsec. If there is an additional 10 nsec delay for propagation from one ALU to the next, how long does it take for the result of a 16-bit add to appear?