Problem 1
Represent each of the following sentences by a Boolean equation

a) The company safe should be unlocked only when Mr. Jones id 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.

c) You should laugh at a joke if it is funny, it is in good tatste, and it is not offensive to others, or if it is told in class by your professor (regardless of whether it is funny and in good taste) and it is not offensive to others.

d) The elevator door should be open if the elevaor is stopped, it is level with the floor, and the timer has not expired, or if the elevator is stopped, it is level with the floor, and a button is pressed.

Problem 2

Find the minimum sum of product for each function using a Karnaugh map.

a) f3 (r, s,t) = r t' + r' s' + r' s
b) f4 (x, y,z) = M0 . M5

Problem 3

a) Plot the following function on a Karnaugh Map. (Do not expand to minterm form before plotting)

F(A, B,C, D) = BD' + B'CD + ABC + ABC'D + B'D'

b) Find the minimum sum of products
c) Find the minimum product of sums

Problem 4

A switching circuit has two control inputs ( C1 and C2), two data inputs (X1 and X2), and one output (Z). The circuit performs one of the logic operations AND, OR, EQU (equivalence), or XOR (exclusive OR) on the two data inputs. The function performed depends on the control inputs:

a) Derive a truth table for Z.
b) Use a Karnaugh map to find a minimum AND-OR gate circuit to realize Z