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’)