Question 1 (15 points): Choose the correct answer: 1- The function can be minimized to: a) b) c) d) 2. The function can be written as: a)! b) 0 3- The POS Boolean expressions that describes the truth table is: A 0 0 0 0 1 1 1 1 ( 0 0 0 0 1 1 0 O 1 1 0 0 0 1 1 1 Output 1 0 0 0 1 0 1 1 1 b) d) 3. 4- Using SOP, the non-essential prime(s) in the following k-map are: CD AB 00 01 11 10 00 0 0 1 1 01 0 0 1 1 11 1 1 0 0 10 1 1 1 0 a) AB'D b) B'CD c) A'BD', BC'D d) AB'D, B'CD 5- A MUX with 4 select lines has: a) I output b) 2 outputs c) 4 outputs d) 16 outputs 6- The following picture represents a/an > 5 94- wa Ya Y! YD AD a) decoder b) encoder c) multiplexer d) demultiplexer Question 5(35 points): You need to design a digital circuit that has three inputs (A, B and C) and one output (F). F is set to one if the input is a prime number and zero otherwise (assume that the number zero will not be used as input that is, invalid). a) Write the truth table. (5 points) b) Using K-map, conclude the simplified form of F. (5 points) c) Implement the circuit using 2-to-4 decoder (5 points) d) Implement the circuit using 3-to-8 decoder. (5 points) e) Implement the circuit using 8-to-1 MUX (5 points) 1) Implement the circuit using 4-to-1 MUX (10 points) Question 2 (15 points): Given the following circuit b d a) Write the minimized form of function F (a, b,c,d). (5 points) b) Draw a NAND only equivalent of the original circuit (10 points) Question 3(10 points): Given the Boolean function F(A,B,C,D) = 2(0,1,4,9,10,11,14) + D(5,7,13,15). a) Draw the k-map and deduce a minimized function in SOP form (5 points) b) Deduce the essential and non-es n-essential prime implicants. (5 points) Question 4 (25 points): Given the following function F (a, b, c)=a'b' + b'c+ab. a) Draw the truth table of F. (5 points) b) Implement the circuit of Fusing one 2-input multiplexer and any additional logic gates. (10 points) c) Implement the circuit of F using 2-input multiplexers an NOT gates only. (10 points)