CSC270 Homework 2 2012
--D. Thiebaut 14:33, 8 February 2012 (EST)
This assignment is due on 2/15/12, at 1:10 pm. You can work on this homework assignment in pairs.
Contents
Problem #1
- Is the exclusive-or gate a universal gate? Why, or why not?
Problem #2
- Assume that we have a gate that implements the function:
f = a . b'
- Is this gate 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. You are allowed to use additional gates, such as and, or or inverter gates.
- Same question with a 4-t-16 decoder with active-low outputs.
Problem #6 (Optional and extra 1/5 point out of a total of 4 for hw)
- 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.
