What is a Boolean Variable? A Boolean Variable is an expression which returns either true or false. 2. Create a table demonstrating...
What is a Boolean Variable?
A Boolean Variable is an expression which returns either true or false.
2. Create a table demonstrating the Boolean Operations complement, addition, and multiplication. { ￣,+,·}
A | B | _____ A + B |
A.B |
A+B |
0 | 0 | 1 | 1 | 1 |
0 | 1 | 0 | 1 | 1 |
1 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 0 | 0 |
note: you can use ’ instead of the overline in this project
3. Calculate the result for the Boolean function: f(x,y) = (x∙y) + (x∙ȳ) for the following inputs
x = 1 and y = 1 : f(1,1) = ?
x = 0 and y = 1 : f(0,1) = ?x
4. How many Boolean functions on two variables are there?
4
5. What does functionally complete mean?
functionally complete is a set of logical connectives or Boolean operators which can be used to express all possible truth tables by combining members of the set into a Boolean expression.
6. What is a literal? Given the Boolean Variables x and y, what are the associated four literals?
7. What is a minterm? Given the Boolean Variables x and y, what are the associated four minterms?
A minterm is a product of literals such that each is either vj or vj’. Each of the variables appearing in a literal is one of the input variables and each input variable appears in one of the literals.
Identify the four functions from the Table 3 that correspond to each minterm.
8. What is disjunctive normal form?
disjunctive normal form is a standardization of a logical formula which is a disjunction of conjunctive clauses; it can also be described as an OR of ANDs, a sum of products.
Given the Boolean Variables x and y, give the Boolean function in disjunctive normal form for functions F9 and F11.
Demonstrate
9. Using the variables x and y, create a table listing all the Boolean functions on two variables. Be sure to give them in
X | Y |
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disjunctive normal form. All other formats will earn 0 points.
10. Using the propositions P and Q, list the equivalent characterizations of your Boolean functions as compound propositions.
Translate from your list above and do not simplify.
10 years ago 20