CSC270 Homework 1

(c) --D. Thiebaut 22:01, 28 January 2009 (UTC)
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This assignment is due on Wednesday evening, at the beginning of Lab 2.

Problem 1

Assume that we define a Boolean Algebra where the two values possible are { α, β }, and where the operators are U, T, and NOT.

The U operator has the following truth table:

x	y	x U y
α	α	α
α	β	α
β	α	α
β	β	β

The T operator has the following truth table:

x	y	x T y
α	α	α
α	β	β
β	α	β
β	β	β

Which of these assertions is true?

• α is 1, β is 0, U is the AND operator, and T the OR operator
• α is 0, β is 1, U is the OR operator, and T is the AND operator

Be sure to explain why one assertion is true, or why it is false!

Problem 2

Expand and simplify the function defined as f(a, b, c, d ) = Σ(0, 1, 2, 8, 10, 12, 13, 14, 15)

Expand and simplify the function defined as g(a, b, c, d ) = Σ( 3, 4, 5, 6, 7, 9, 11 )

Make sure you use your head and think!!!

Problem 3

• What is the function Q( A, B, C ) implemented by the circuit shown to the right, where the gates are NAND gates (an AND gate combined with a NOT gate on its output)?
• What is the diagram of Q using only NOT, OR, and AND gates?
• What is the minterm canonical form of Q?