CSC270 Exercises on Karnaugh Maps, and Decoders

Exercise 1

• Using Karnaugh maps, design the following circuit with as few gates as possible: f = Σ( 2, 9, 11 )

Exercise 2

• Same question, for f = Σ( 2, 9, 11 ). However, this time we know for certain that the two signals a and b will never have the same value as c and d. In other words, if a and b are 0 1, then c and d cannot be 0 1.

Exercise 3

• Same question with g = Π( 5, 7, 13, 15 ).

Exercise 4

• Implement f of Exercise 1 with a 3-to-8 decoder with active-high outputs, and an active-high enable.

Exercise 5

• Implement 'g of Exercise 3 with a 3-to-8 decoder with active-low outputs and an active-low enable.

Exercise 6

• Implement a 3-to-8 decoders with several 2-to-4 decoders that have active-high outputs and an active-high enable input.

Exercise 7

• Implement f=Σ(2,5) with a 4-to-1 multiplexer.
• Implement g = Σ( 0, 1, 10, 14, 15) with a 4-to-1 multiplexer