CSC270 Homework 2 2012

--D. Thiebaut 14:33, 8 February 2012 (EST)

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This assignment is due on 2/15/12, at 1:10 pm. You can work on this homework assignment in pairs.

Problem #1

• Is the exclusive-or gate a universal gate? Why, or why not?

Problem #2

• is the gate that implements f = a . b' a universal gate? Why, or why not?

Problem #3

• f = Σ( 1, 2, 13, 14, 15). What is the Maxterm canonical form for f?
• g = Π( 0, 1, 2, 3, 4, 5, 6, 7 ). What is the Minterm canonical form for g?

Problem #4

• Using Karnaugh maps, simplify the following functions:
  • f = Σ( 0, 1, 2, 3, 4, 12, 13, 14, 15 )
  • g = Σ( 0, 15 ) + Π( 5, 6, 12, 13, 14, 15 ) (here, + is the or operator)
  • h = Σ( 0, 5, 6, 10, 11, 12, 13, 14 )

Problem #5

• Implement f = &Sigma( 1, 10, 11, 13, 14, 15 ) with a 4-to-16 decoder with active-high outputs.
• Same question with 4-t-16 decoders with active-low outputs.

Problem #6 (Optional and extra 1/5 point credit)

• Same question as Problem #5, but assume we do not have 4-to-16 decoders, but we have a lot of 3-to-8 decoders, some with active-low outputs, and some with active-high outputs.