CSE370 Assignment 4

Distributed: 6 February 2001
Due: 14 February 2001

Reading:

• Lecture Notes V (Combinational Logic Case Studies): Slides 1-32.

Exercises:

1. Katz 4.2. Print the PAL schematic (see Materials below) and mark inputs, outputs, and connections. Ignore tri-state buffers.
2. Katz 4.15. Implement F' instead.
3. Show there are at least 6 different 3-bit Gray code sequences that start from 000. Implement a circuit that has 6 inputs ABCDEF and an output GHJ. Output GHJ=NextGrayCodeSequence(ABC, DEF) where DEF is the selector for one for the six different Gray code sequences. Use 3-bit Gray code blocks equal to the one created in Assigment 3.
4. Katz 4.27.
5. Katz 5.13. a) and b).
6. Katz 5.17.
7. Exactly as one can define a real variable by an equation which needs to be solved for the given variable (for example 2x^2 + x - 2 = 0), one can also define a boolean function by giving an equation which needs to be solved for the unknown boolean function. For example, if S and T are given boolean expressions, one might define the boolean function f by requiring that S * f = T. Note that, exactly as in the real number case, there might be more than one distinct boolean function f that solves the equation (two functions are said to be distinct if one cannot be derived from the other using Boolean algebra; alternatively, if they have different truth tables).
   Let R and S be 3-input functions that you have defined and that are distinct from the functions given in last quarters Assignment 4.
   Show how to derive all possible boolean functions f1...fn that satisfy the equation R * f = S. 
8. Construct a schematic diagram for the functions that appear on slide #23 of the Combinational Logic lectures.  (See Notes for Lectures 3-6: HTML or PDF.)  Assign a delay of 1 to inverters, 2 to 2-inputs AND and OR gates, 4 to 3-input AND and OR gates, and 6 to XOR gates.  Use the DesignWorks simulator to create waveforms similar to those on slide #26.  Turn in a printout of the waveforms and explain why the waveforms have the shape they have and why they differ from those on slide #26.
9. Implement the 2-bit multiplier function (i.e., 2-bit number AB times 2-bit number CD yields 4-bit number WXYZ) using 4 16:1 multiplexers. Show your truth table and how you derived the inputs to the multiplexers. Now reimplement the circuit using 4 8:1 multiplexers controlled by the inputs A, B, and C (you can assume that D and D' are available). In addition to these circuits, turn in a DesignWorks schematic that uses the Mux-8 devices in the Primlog library  to implement the W, X, and Z outputs (make sure to tie the EN input of the multiplexers to 0 to enable their operation - you can use another switch for this).

• A printable PAL schematic (pal.jpg or pal.pdf) from Katz page 217.

Rationale:

• To understand the time behavior of digital circuits.
• To practice mapping of Boolean functions onto regular combinational logic structures.