Homework #4 September 7,2005 - Name ___________________
#1. Use a table to express the values of each of the following Boolean function
F(x,y,z) = x'y + y'z
|
y' |
x' |
x |
y |
z |
x'y |
y'z |
F(x,y,z) =x'y + y'z |
|
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
|
1 |
1 |
0 |
0 |
1 |
0 |
1 |
1 |
|
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
|
0 |
1 |
0 |
1 |
1 |
1 |
0 |
1 |
|
1 |
0 |
1 |
0 |
0 |
0 |
0 |
9 |
|
1 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
|
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
|
0 |
0 |
1 |
1 |
1 |
0 |
0 |
0 |
#2. How many different Boolean functions are there of degree 6?
2 to the 2 to the 6th OR
264
#3. Find the duals of these Boolean expressions
a. x + y xy
b. x'y' x + y
4. Find a Boolean product of the Boolean variables x, y, and z, or their complements that has the value 1 if and only if:
x = z = 0, y = 1
xyz
#5. Study example 3 on page 710 carefully and then do the following problem. (Note: I do not require you to use the Boolean identities to produce the answer; you may use the table).
Find the sum-of-products expansion of the Boolean function below
F(x,y) = x' + y
xy + xy + xy
#6. page 718 problem 2.
(xy)
#7. page 16, problem 8a (section 1.1)
If you have the flue, then you miss the final exam
#8. page 26, problem 8c (section 1.2)
|
p |
q |
p -> q |
p^(p->q) |
[p^(p->q)]->q |
|
0 |
0 |
1 |
0 |
1 |
|
0 |
1 |
1 |
0 |
1 |
|
1 |
0 |
0 |
0 |
1 |
|
1 |
1 |
1 |
1 |
1 |
#9. page 41, problem 14a (section 1.3)
TRUE when x = -1
#10 p 52, problem 8 a (section 1.4)
$x$y (Q(x,y))