Boolean-algebra.docx

CLASSS :12

CYCLE TEST

SUB: COMPUTER SCIENCE

Marks:30

1) A) Convert the following Boolean expression into its equivalent canonical Sum of Product Form: (X’+Y+Z’).(X’+Y+Z).(X’+Y’+Z).(X’+Y’+Z’) (2) B) Reduce the following Boolean expression using K-map: F(A,B,C,D) = Ʃ(0,2,3,4,5,6,7,8,10,12) (3) C) Draw the logical circuit for the following Boolean expression X’.(Y’+Z) (2) D) Write the dual of the Boolean expression (U + W)(V’U + W) (1) 2) A) Correct the following statements; (2) i) X+1 = Y ii) (A’)’ = A’ iii) A+A’ = 0 iv) (A+B)’A.B B) Draw the logical circuit for the following Boolean expression (A.B)+C (2) C) Write the POS form of a Boolean Function F which is represented in a truth table as follows; (1) P Q R F 0 0 0 0 0D 0 1 1 0 1 0 1 D) Reduce the following Boolean expression using K-map 0 1 1 1 F(A,B,C,D) = Ʃ(0,1,3,5,6,7,9,11,13,14,15) (3) 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 3) A) State and verify Absorption law algebraically; (2) B) Draw the logical circuit for the following Boolean expression A.B+C.D’ (2) C) Write the SOP form of a Boolean Function F which is represented in a truth table as follows; (1) A B C D 0 0 0 0 0 0 1 1 D)Obtain a simplified Form for the Boolean expression 0 1 0 1 F(U,V,W,Z) = π(0,1,3,5,6,7,15) (3) 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 4) A) Draw the logical circuit for the following Boolean expression Using only NOR gates (A+B).(C+D) (2) B) Derive the Canonical POS form for a Boolean Function G which is represented in a truth table as follows;(1) A 0 0 0 0 1 1 1 1

B 0 0 1 1 0 0 1 1

C 0 1 0 1 0 1 0 1

D 0 0 1 0 1 1 0 1

C)Obtain a simplified Form for the Boolean expression E(U,V,W,Z) = π(2,3,6,8,9,10,11,12,13)

(3)