1. [10] The behavior of the overhead dome light in a vehicle is con...

1. [10] The behavior of the overhead dome light in a vehicle is controlled by a three position switch. When in the "off" position, the dome light is never illuminated. When in the "on" position it is always on. When in the "door" position it is turned on only when one or more of the two front doors is open. There is a sensor for each door that generates a signal that indicates the door is open. The inputs are SwitchOn, SwitchOff, SwitchDoor (exactly one will be 1 to indicate the position of the switch) and DriverDoorOpen and PassengerDoorOper which are one when the indicate door is open. Create a Boolean equation for the output of a circuit that will turn on the dome light given these inputs. 2. [10] Show the truth table for the function f2 x x y. 3. [16] Consider the truth table below. a) Express the function t f1 in compact minterm form. b) Express the function f1 in canonical sum of products form. c) Express the function f1 in compact maxterm form. d) Express the function f1 in canonical product of sums form. e) Express the function f2 in compact minterm form. f) Express the function f2 in canonical sum of products form. g) Express the function f2 in compact maxterm form. h) Express the function f2 in canonical product of sums form. x y Z Function f Function f2 i) i) I 1 1 1) 1 1 1 I 1 1 1 I i) 1 I I I I I 4. [10] You're involved in the design of a hand-held device to play blackjack ("21"). In addition to a 2- bit value for encoding the suit (e.g. hearts, diamonds, spades, and clubs) which need not concern us here, you are using a 4-bit code (b3,b2,b1,bo) to represent the value of a card, with 0000 unused but ace represented by 0001, two by 0010, etc. through ten. Jack, Queen, and King are represented by 1011, 1100, and 1101 respectively. The other 4-bit code values are unused. In blackjack the value of face cards (Jack, Queen, and King) as well as the ten card is 10. Create a truth table for the function F that is a 1if the card has a value of 10 and is otherwise. Any unused input combinations should yield 0. 5. [10] Write the canonical SOP form for the function in problem (4) above. 6. [15] Use a K-map to minimize the function F(x,y,z) 7. [15] Use a K-map to minimize the function from problem (4) above. 8. [15] Use Xs instead of Os for the unused input combinations in the truth table for problem 4 above and minimize the function. 9. [15] Use a K-map to minimize the function F (A,B,C,D) = A B. E C D A B C D + A E C 10. [15] Minimize the function for problem (9) above in POS form. 11. [15] Use a K-map to find a minimum SOP expression for the function F(w,x,y,- =(1,3,7,11,15)+md(0,2,5). 12. [15] Use K-maps to produce a minimized SOP equation for the function F (V, W, x,y,2) = (0,1,4,5,6.8.9,12,13,14,15,16,17,18,20,21,24,25,26,28,29,31)