Tutorial-2                                              Digital logic design

B.E.3^rd sem CO                                                       Date:08/08/2013

 

Q.1 Reduce the expression to a minimum numbers of literals.

1.     A+B(AC+(B+C’)D)         2. xyz + x’y +xyz’

3.        (A+(BC)’)’(AB’+ABC)   4. (A+C+D)(A+C+D’)(A+C’+D)(A+B’)

5.        A′B′CE′ + A′B′C′D′ +B′D′E′ + B′C D′  6. (A+B)’(A’+B’)’

Q.2  

1.     Explain with figures how NAND gate and NOR gate can be used as Universal gate.

2.     Draw symbol and construct the truth table for three input Ex-OR gate.

3.     What is the principle of Duality Theorem?

4.     Implement Boolean expression for Ex-OR gate using NAND gates only.

5.     Obtain the truth table of the function F1 = xy+y’z+xy’

 

Q.3 Demonstrate by means of truth tables the validity of the following theorems of Boolean algebra :      (i) De Morgan’s theorems for three variables

                             (ii) The Distributive law of + over-

                                      (iii) The associative laws

 

Q.4 Implement the following Boolean functions

          (i) F= A (B +CD) +BC′ with NOR gates

          (ii) F= (A + B′) (CD + E) with NAND gates

 

Q5 Draw the logic symbol and construct the truth table for following gates.

 [1] Two input NAND gate [2] Three input OR gate

[3] Three input EX-NOR gate [4] NOT gate

 

Q.6

1.     Explain briefly: standard SOP and POS forms using suitable examples.

2.     What are Minterms and Maxterms?

3.     Express following Function in Product of Maxterms

F(x,y,z)= ( xy + z ) ( y + xz )

 

Q.7 Obtain the simplified expressions in SOP & POS for the following Boolean functions using k-map

1.     F(w,x,y,z)  =  Σ (0,1,2,4,5,6,8,9,12,13,14)

2.     F(w,x,y) = Σ (0,1,3,4,5,7)

3.     F = A’B’C’+B’CD’+A’BCD’+AB’C’

4.     F =A’B’D’+A’CD+A’BC  d=A’BC’D+ACD+AB’D’

5.     F( w,x,y,z) = Σ( 1 , 3 , 7 , 11 , 15 ) with  d( w,x,y,z ) = Σ( 0, 2 ,5 )

6.     F= (a’ + b’ + d)(a’ + d’)(a + b + d’)(a + b’ + c+ d)

7.      F(p,q,r,s)= Σ( 2,3,12,13,14,15 )

8.     F= Σ(0,1,4,5,10,11,12,14) and

9.      F=Σ(11,12,13,14,15).

 

Q.8  Simplify given function & implement it with 1. NAND gates only 2. NOR-OR  3. NAND-AND  4. OR-NAND  5. AND-NOR

F=(B’ + D’)(A’ +C’ +D)(A+B’ +C’ + D)(A’ + B+C’ +D’)

 

Q.9 Simplify Boolean function F ( w,x,y,z ) = Σ ( 0,1,2,4,5,6,8,9,12,13,14 ) using K-map and Implement it using (i) NAND gates only (ii) NOR gates only.

 

Q.10

	1.     Find the complement of the following Boolean function and reduce to a minimum number of literals. B’D  F = B’D+A’BC’ + ACD + A’BC
	2.     Obtain the simplified expressions in sum of products using K-map: x’z + w’xy’ + w(x’y + xy’)

NOTE: last date of submission is 22/08/2013