# CSC347-ENS211 Homework #2 Solved

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1. Demonstrate by means of truth tables the validity of the following identities:

The distributive law: x + yz = (x+y)(x+z)

1. 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’

1. Find the complement of the following expression

(a) (A’+B)C’           (b) (AB’ + C)D’ + E

1. Draw the logic diagram for the following Boolean expressions:

(a) Y = AB + B’(A’ + C)               (b) Y = (A + B’)(C’+ DE)

1. Obtain the truth table of the function F = (A+ C)(B’ + C) and express the function in sum of minterms and product of maxterms.

1. Express the following function in sum of minterms and product of maxterms:

F(a, b, c, d) = (c’ + d)(b’ + c’)

1. Convert the following to the other canonical form:

(a) F(x, y, z)                       (b)

1. Convert the following function into sum of products and product of sums. You need to simplify it first.

F =  (BC + D)(C + AD’)

1. 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

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