CSC270 Homework 3

© D. Thiebaut, 2009

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This assignment is due on Wednesday evening, at the beginning of Lab 4.

Exercise 1

Assume that we have a boolean function f(a, b, c, d) = Σ( 5, 7, 15 ).

What is its minimal form, as given by a Karnaugh map?

Assume furthermore we know that the the signals a and b are never both equal to 1 at the same time, and that c and d are never both equal to 00 at the same time. So, for example, the signals a, b, c, d will never be in the state 1 1 0 1, because that would require a, and b to be 1. Similarly, the condition a = 0, b=1, c=0, d=0 will never occur either, because c and d are 0 in this case.

How can we use this information to our advantage, as logic designers?

Exercise 2

What is the simplified expression of the function g(a, b, c, d, e) expressed by the Karnaugh map above?

Exercise 3

Draw the logic diagram for the functions h() and k() below with 4-to-1 multiplexers:

• h( a, b, c, d ) = Σ( 0, 1, 2, 3, 4, 6, 12, 14 )

• k( a, b, c ) = &Sigma( 0, 1, 2, 3, 7 )

Draw the logic diagram of the same functions with 8-to-1 multiplexers.

Exercise 4

Implement a 16-to-1 multiplexer with only 4-to-1 multiplexers.