# CSC270 Homework 2 2012

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--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.

# 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.