Assignmnet on Boolean Algebra

Q.1 Which gates implement logical addition, multiplication and complementation.
Q.2 Which of the following Boolean equations is/are incorrect ? Write the correct forms of the incorrect ones after showing why are they incorrect–
i) A + A’ = 1 ii) AA’=1 iii) A(A + B)’= A
iv) (AB)’ = A’B’ v) A+A’B = A+B vi) (A+B)’= A’+ B
Q.3 When does a XOR gate produce high output? When does a XNOR gate produce high output?
Q.4 What would be the complement of the following –
i) A’(BC’+B’C) ii) xy + yz’ + z’z
Q.5 Prove (giving reasons) that ((x+y)’+(x+y)’)’ = x + y
Q.6 Write the Boolean expression for a logic network that will have a 1 output when X=1,Y=0,Z=0; X=1,Y=0,Z=1; X=1,Y=1,Z=0; and X=1,Y=1,Z=1
Q.7 Draw the logic circuit for a’b’cd + abc’d + ab’cd using only NAND gates.
Q.8 Draw the logic circuit for (a’+b’+c+d)(a+b+c’+d)(a+b”+c+d) using only NOR gates.
Q.9 Draw logic circuits for the following –
a) F(A,B,C,D) = Minterms of (1,3,5,8,10,12) , Minterms of (0,1,2,4,5,6,8,10)
b) F(W,X,Y) = maxterm of (0,2,4,6,7)
Q.10 Seven inverters are cascaded one after another. What is the output if the input is 1 ?
Q.11. Write the equivalent boolean expression for the cicuit.