problem 1:

a) Show that the dual of the exclusive – OR is equal to its complement
 
b) Prove that if w’x+yz’= 0, then wx+y’(w’+z’) = wx + xz + x’z’ +w’y’z
 
c) Find out the Canonical SOP representation of the functions:

i) f (x,y,z) = z+(x’y) (x+y’)

ii) f (x,y,z) = x + (x’y’+x’z)’
 
problem 2:

a) Given the following Boolean function. F = xy’z + x’y’z+w’xy+wx’y+wxy

i) Obtain the truth table of the function.
ii) Draw the logic diagram using the original Boolean function.
 
b) Simplify the given Boolean expressions to a minimum number of literals:

i) x’ y’ + xy + x’y

ii) x’y+xy’+xy+x’y’

iii) (x+y) (x+y’)

iv) x’ + xy + xz’ + xy’ z’

c) Find out the complement of the given expressions:

i) xy’ + x’y

ii) ab (c’d+cd’) +a’b’(c’+d) (c+d’)

problem 3:

a) Express the following functions in sum of minterns and product of maxterms.

i) F(a,b,c,d) = b’d+a’d+bd

ii) f(x,y,z) = (xy+z) (xz+y)
 
b) Draw the logic diagram of the given Boolean expression:

F(x,y,z) = xy’z + x’yz + xyz + xyz’

c) Reduce the given Boolean expressions to the indicated number of literals:

i) a’c’ + abc + ac’ – (3)

ii) (x’y’+z)’ + z+xy+wz – (3)

problem 4:

a) Draw the logic diagram corresponding to the given Boolean expression:

bc’ + ab+acd
 
b) Draw the logic diagram corresponding to the following Boolean expression:

(a+b)(c+d)(a’b+d)
 
c) Convert the given to the other canonical form:

i) (ab+c) (b+c’d)

ii) x’+x(x+y’) (x+z’)