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Exercise_Midterm1

Exercise_Midterm1 - m(0,1,3,9,11,12,14,15 b f(A,B,C,D = π...

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CSE140 Exercises 10/9/2010 1. (Laws and Theorems of Boolean Algebra) Simplify the following using Boolean algebra and write the particular law you are using in each step. a. F (A, B, C) = A'B'C'+AB'C'+ABC'+ABC+A'B'C+AB'C b. F (A, B) = (A'+B) (A+B) 2. (Laws and Theorems of Boolean Algebra) Prove the following using Boolean algebra and write the particular law you are using in each step. a. a'b' + a'c' + bc' = a'b' + bc' b. (a'+ b)(a'+ c')(b'+ c') = (a'+ b)(b'+ c') 3. Canonical Expression: A counter inputs four bits (A,B,C,D) and outputs three bits Y=(y2,y1,y0). The output Y is the binary code of the number of "1"s in the inputs. a. Write the truth table of the counter. b. Express the outputs in the form of the sum of minterms. c. Express the outputs in the form of the product of maxterms. 4. (Karnaugh Map) Use K-map method to simplify the function and write all possible minimal sum of products expressions. a. f(A,B,C,D) =

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Unformatted text preview: m (0,1,3,9,11,12,14,15) b. f(A,B,C,D) = π M(2,5,6,8,9,10) * π D(4,11,12) 5. (Karnaugh Map) Use K-map method to simplify the function and write all possible minimal product of sums expressions. a. f(A,B,C,D) = π M (0,1,6,7) b. F(A,B,C,D) = ∑m(1,3,5,7,9) + ∑ D(6,12,13) 6. (Universal Set of Gates) Check if the set in the following list is universal and explain your decision. Assuming constants 0 and 1 are available as inputs. a. {NAND} b. {f(x,y,z)} where f(x,y,z) = xy' + yz 7. (Shannon Expansion) Prove using Shannon’s Exapnsion (f is the function): a. F(x,y,z) : x'y'z'+x'y'z+x'yz+xy'z'+xy'z = y’ + x’yz b. F(x,y) : (xy + x'y) XOR (x'+y) = x’y’ 8. (Karnaugh Map) Use K map to simplify function f ( a , b , c , d ) = ∑ m (0,1, 2, 3, 4, 5, 7,8,12)+ ∑ d (10,11). List all possible minimal two-level sum of products expressions. Show the switching functions. No need for the diagram....
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