Demonstrate by means of truth tables the validity of the following identities:
The distributive law: x + yz = (x+y)(x+z)
Simplify the following Boolean expressions to a minimum number of literals.
(a) (a + b + c’)(a’b’ + c) (b) a’bc + abc’ + abc + a’bc’ (c) (a’ + c’)(a + b’ + c’)
(d) ABC’D + A’BD + ABCD (e) AB’ + A’B’D + A’CD’
Find the complement of the following expression
(a) (A’+B)C’ (b) (AB’ + C)D’ + E
Draw the logic diagram for the following Boolean expressions:
(a) Y = AB + B’(A’ + C) (b) Y = (A + B’)(C’+ DE)
Obtain the truth table of the function F = (A+ C)(B’ + C) and express the function in sum of minterms and product of maxterms.
Express the following function in sum of minterms and product of maxterms:
F(a, b, c, d) = (c’ + d)(b’ + c’)
Convert the following to the other canonical form:
(a) F(x, y, z) (b
Convert the following function into sum of products and product of sums. You need to simplify it first.
F = (BC + D)(C + AD’)
Use Boolean algebra to prove that the following Boolean equalities are true:
(a) a’ b’ + ab’ + a’b = a’ + b’
(b) (a + b)’bc = 0
(c) (ab’ + a’b)’ = a’b’ + ab
