Homework # 2 - Math 2236
The problems on this homework must be done alone. The honor code is in effect.
You may submit the solutions twice, if you wish.
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Questions 1 - 7 deal with the following set of logic gates.
In this image, a and b are the imputs and q is the output. Each is a boolean variable and can take the values 0/F or 1/T. You can see the line from a splits so that it goes into both the AND gate and the top NOT gate. And the line from B splits, too. The place where the line from A bends over the line from B means that there, the connections don't touch.
1. Find q if a = 0 and b = 0.
a. 0
b. 1
2. Find q if a = 1 and b = 0.
3. Find q if a = 0 and b = 1.
4. Find q if a = 1 and b = 1.
5. What does this system of logic gates tell you?
a. a OR b
b. a AND b
c. a XOR b
d. a = b
6. How would you write this system of logic gates in mathematical notation?
a. q = (a AND b) AND ((NOT a) OR (NOT b))
b. q = (a OR b) AND ((NOT a) AND (NOT b))
c. q = (a AND b) OR ((NOT a) AND (NOT b))
d. q = (a OR b) AND ((NOT a) OR (NOT b))
7. Which of these is logically equivalent to the original system of logic gates (in other words, it has the same truth table)?
a. NOT (a AND b)
b. NOT (a XOR b)
c. NOT (a OR b)
d. (NOT(a) OR NOT(b))
8. Write the prime factorization of 6000. What power is the prime 2 raised to?
a. 2
b. 3
c. 4
d. 5
9. Use your prime factorization of 6000 to tell you how many prime factors 6000 has.
a. 30
b. 40
c. 60
d. 80
e. 120
10. Find the greatest common divisor of 6000 and 4375 (it will help if you find the prime factorization of 4375 first).
a. 25
b. 50
c. 75
d. 125
e. 625
11. Find the least common multiple of 6000 and 4375 (it will help if you find the prime factorization of 4375 first).
a. 24,000
b. 105,000
c. 210,000
d. 420,000
e. 630,000
12. In a bin of cups, 14 have handles, 12 are made of glass, and 3 both have handles and are made of glass. How many cups either have handles or are made of glass?
a. 23
b. 24
c. 25
d. 26
e. 29