I don't know if these questions are associated with this particular website, but I will ask them anyway just in case. If you can help me, please do so!

1.) Prove the following equivalence statement using Boolean equivalence laws. Don't forget to identify the individual laws applied at each step.

_________

__ _ _

(AB)(A + B) = A B + AB

Not(Not A and B)(A or B) = Not A and Not B or A and B

The Not over the whole thing is confusing me.

3.) For the following truth table, (a) rewrite the function in the sum of products minterm form, (b) express the function as a Boolean sum of products, (c) minimize the expression using a 2 variable Karnaugh map, and (d) draw the minimized circuit.

Truth table:

C F | Z

0 0 1

0 1 0

1 0 1

1 1 1

I did this problem, but I am just wondering if I did it right. Here's what I have (E = summation, m = minterm symbol):

(a) Z(C, F) = E m(0, 2, 3)

_ _ _

(b) Z = C F + C F + C F (Z = Not C AND Not F OR C AND Not F OR C AND F)

_

(c) Z = F + CF (minimized expression using equivalence laws - I don't really understand how to get an expression out of the Karnaugh map)

(Z = Not F OR C AND F)

4.) Given the following Boolean function, (a) rewrite the function in the sum of products minterm form, (b) express the function as a Boolean sum of products, (c) minimize the expression using a 3 variable Karnaugh map, and (d) draw the minimized circuit.

Given Boolean function (O+ = exclusive or):

___________ _

Y = (D + (E O+ F))(DF + E) (NOT(D OR (E XOR F)))(D AND F OR Not E)

I don't even know where to start on this one.

5.) A digital circuit we've developed is represented by the function W below. It was recently discovered, however, that input minterms 1, 2, 8, 10, and 11 were physically impossible when the circuit is used in a machine. Develop a new Boolean expression for W that is a minimized sum of products with the "don't care" minterms (the X's in a Karnaugh map) taken into account.

_ _ ___ ___ _ _ _ _

W = A B C D + A B C D + A B C D + A C D + A B C

(Not A AND Not B AND Not C AND D OR A AND B AND NOT C AND D OR A AND NOT B AND NOT C AND D OR NOT A AND C AND D OR NOT A AND B AND C)

Are the "don't care" (X's) the minterms 1, 2, 8, 10, and 11?

Where do I start? Do I draw a Karnaugh map first? How do I know what is a 1 and what is a 0 in it?

If anyone can help me, it would TRULY GREATLY be appreciated. Thanks.