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Boolean Algebra and Computer Logic
o n t H e c o m p u t e R
For Exercises 1–4, write a computer program that
produces the desired output from the given input.
1. Input: n and tables defining two binary operations
and one unary operation on a set of n objects
Output: Indication of whether the structure is a
Boolean algebra
Algorithm: Testing the 10 properties for all cases
2. Input: n, tables defining a binary operation on each
of two sets of n elements, and a table defining a
bijection from one set to the other
Output: Indication of whether the function is an
isomorphism
Algorithm: Testing all possible cases
section 8.3
1. A Karnaugh map is a device to help change a
canonical sum-of-products form to a reduced sumof-products form.
2. The 1s in a Karnaugh map correspond to the 1
values of the truth function.
3. When using a Karnaugh map to reduce a Boolean
expression, the largest possible blocks should be
determined first because they provide the greatest
reduction.
4. In the Quine–McCluskey procedure, terms that
combine must have dashes in the same locations.
5. In the Quine–McCluskey procedure, a check in
some row of the comparison table indicates that
the term for that row is an essential term that must
appear in the reduced expression.
3. Input: n and a table representing a truth function
with n arguments
Output: Canonical sum-of-products Boolean expression for the truth function
4. Input: n and a table representing a truth function
with n arguments
Output: Minimal sum-of-products Boolean expression for the truth function
Algorithm: Using the Quine–McCluskey procedure