Assignment 4

 

Reading Assignment: Notes for Week 3. Chapter 2 and Chapter 3 of Brown and Vranesic.
Notes:

 

For all exercises using Boolean algebra in the following, show all the steps and state explicitly all axioms/theorems/properties that you used. 

 

 

  1. (10 points) Problem 2.37 in Brown and Vranesic.

 

  1. (10 points) Problem 2.39 in Brown and Vranesic.

 

  1. (10 points) Write Verilog code for a full adder circuit with three input and two outputs.

 

  1. (20 points) (a) Problem 3.1 in Brown and Vranesic. (b) Problem 3.2 in Brown and Vranesic.

 

  1. (10 points) Problem 3.7 in Brown and Vranesic.

 

  1. A function f has four inputs a, b, c, d and one output such that the output is a 1 if and only if the number of 1s in the inputs is even.

(a)    (6 points) Derive the truth table for f.

(b)   (5 points) Derive a sum-of-products expression for f using Karnaugh map.

(c)    (5 points) Derive a product-of-sums expression for f using Karnaugh map

(d)   (6 points) Draw the circuits in (b) and (c) using and-or and or-and logic as appropriate.

(e)    (6 points) Draw the circuits in (b) and (c) using nand and nor gates only as appropriate.

(f)     (6 points) Draw a PLA implementation for circuit in (b).

(g)    (6 points) Draw an FPGA circuit for circuit using a 4-LUT.