**PART I**

**Answer all questions**

**Question 1**

(a) State the DeMorgan’s Laws. Verify any one of them using truth table. [2]

(b) Using a truth table, verify if the following proposition is valid or invalid: [2]

(A→B) ^ (B→C) = (A→C)

(c) Find the compliment of: F(A,B,C,D)= [A + { ( B+C) . (B’+ D’)}] [2]

(d) If A=1 and B=0, then find : [1]

i) (A’+1).B

ii) (A+B’)’

(e) What is maxterm and minterm? [1]

(f) Reduce the following to its simplest form using laws of Boolean Algebra. At each step state the law used for simplification. AB’+A’BC’+(AC)’+BC [2]

**PART II**

**Question 3 [10]**

a) Given the Boolean function F( A, B, C, D) = π(0, 1, 2, 3, 5, 7, 8,9,10,11)

i) Reduce the above expression by using 4 –variable Karnaugh map, showing the various groups ( i.e. octal, quads and pairs). [ 4 ]

ii) Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs. [ 1 ]

b )Given the Boolean function : F(A,B,C,D ) = ∑(0,2,4,5,8,9,10,12,13)

i) Reduce the above expression by using 4-variable K-map, showing the various groups (i.e. octal, quads and pairs). [ 4 ]

ii) Draw the logic gate diagram of the reduced expression. Assume that the variables and their complements are available as inputs. [ 1 ]