ONLY SOLVE QUESTIONS 4 AND 5!!!!!!!!!!!

Problem 1. (10 points)

Represent each of the following sentences by a Boolean equation: a) The company safe should be unlocked only when Mr. Jones is in the office or Mr. Evans is in the office, and only when the company is open for business, and only when the security guard is present.

b) You should wear your overshoes if you are outside in a heavy rain and you are wearing your new suede shoes, or if your mother tells you to.

Problem 2. (20 points)

A switching circuit has four inputs as shown. A and B represent the first and second bits of a binary number N1. C and D represent the first and second bits of a binary number N2. The output is to be 1 only if the product N1 N2 is less than or equal to 2.

a) Find the minterm expansion for F.

b) Find the maxterm expansion for F.

Express your answers in both decimal notation and algebraic form.

Problem 3. (25 points)

Given: F(a, b, c) = abc + b.

(a) Express F as a minterm expansion. (Use m-notation.)

(b) Express F as a maxterm expansion. (Use M-notation.)

(c) Express F as a minterm expansion. (Use m-notation.)

(d) Express F as a maxterm expansion. (Use M- notation.)

Problem 4. (25 points)

Work Problem 3 using:

F(a,b,c,d) = (a + b + d)(a + c)(a + b + c)(a + b + c + d) (Continuation in the next side)

Problem 5. (20 points) For given truth table:

a) Find the simplest expression for F2 and specify the values for the dont care lead to this expression.

b) Repeat for F3.