Assignment - 2 Logic Gates, Boolean Expression, Simplification using boolean algebra, Karnaugh's Map ( K Map),

1. Prove that NAND and NOR gates are universal gate.

2. State and Prove De Morgan’s theorems for 3 variables using perfect induction method.

3. Simplify below expressions, and draw a block diagram of the circuit for simplified expression.

a. AB’C’ + A’B’C’ + A’BC’ + A’B’C

b. (A+B+C)(A+B’+C’)(A+B+C’)(A+B’+C)

c. A(A+B+C) (A’+B+C) (A+B’+C) (A+B+C’)

d. (AB’+A’B+AC’)(A’B’+AB’+AC’)

4. Convert following expressions to sum of products form.

a. (A+B)(B’+C)(A’+C)

b. (A’+C) (A’+B’+C’)(A+B’)

5. Convert following expressions to product of sum form.

a. AB + A’(B+C’)(D+B’)

b. (B + C)[(B’ + C’)(A + C’)(B + C )]

6. Write a boolean expression is sum of products form for a logic network that will have a 1 output when x=1,y=0,z=0 ; x=1,y=1,z=0 ; x=1,y=1,z=0 ; x=1,y=1,z=1 ; and 0 output for all other sets of input values. Simplify the expression derived and draw a block diagram for the simplified expression.

7. Derive a Boolean expression in SOP form for 3 variable function. Function generates output 1 when number of 1s are more than number of 0s in an input.

8. Simplify below expressions using K Map method.

a. AB + AC’ + ABC’ + AB’C

b. F(w,x,y,z) = ∑(0,2,6,7,8,10,14,15)

c. F(w,x,y,z) = ∑(1,3,5,8,9,10,13) +d(2,6,11,12)

d. F(w,x,y,z) = ∑(m_n ) where n = 0 to 15

9. Simplify below expression in POS form using K map method

a. F(a,b,c,d) = ∑(3,7,11,13,14,15)

b. F(w,x,y,z) = ∑(0,2,4,6,8,10,12,14)

Prof. V. A. Gandhi