Make logic circuit for the following Boolean expressions:
i) (x′.y + z) + (x+y+z)′ +(x+y+z)
X Y Z
O
ii) ( x'+y).(y′+ z).(y+z′+x′)
X Y Z
O
b) What is dual of a Boolean expression? Find dual of boolean expression of the
output of the following logic circuit:
Ans: If p is a proposition involving ~, ∧ and ∨, the dual of p, denoted by pd, is the proposition
If p is a proposition involving ~, ∧ and ∨, the dual of p, denoted by pd, is the proposition
obtained by replacing each occurrence of ∧ (and/or ∨) in p by ∨ _________ __________ __________ __________ __________ _____ __________ ____ ______ ________ _________ _____.
________ ___ _____ _________ _________ _____ ______ _________ ___ _____ _________ _____.
_______ _____ ____ __________ _______.
_____ ______ __________ ____ ___ ___ ___.
________ ___ __________ ________ __________ __________.
_____ ___ __________ _____ ____ _____ _____ _____ ______.
_____ ___ _______ __________ ____ ___ _______ _____ _____.
______ _________ _____ ____ _____ ________ ______ _______ __________ ________ ___.
____ __________ _________ __________ ________.
__________ _____ __________ ________ ______.
___ ______ _________ _______ _______ ________ _________.
_________ _______ _______ ___ _______.
____ ______ _____ __________ _________ _______ _________.
_____ ______ ____ ____ ___ ___ ______ _______ ________ __________ __________.
_______ _____ __________ ________ ________ __________.
___ ______ __________ _______ _________.
___ ______ _____ _________ ____ ___ _______ ______ ______ ______.
______ _____ ____ ___ ___ ____ ________ ___ _______.
_______ ____ ________ ____ ___ _____ __________ _____ ______.
____ ________ ____ ___ _________ _________ _________ ____.
_______ __________ _________ ___ ___.
______ __________ __________ __________ _____ _______ ___ ___ __________ _____ ___ __________.
________ ______ _______ _________ _______ _____ __________ _____ ___ _____.
_______ _________ ______ ________ _______ ___ ______.
___ ____ ___ ______ ____ ___ ___.
__________ __________ ________ _________ __________ ______ ________ _________ _____ ________.
__________ ________ ______ __________ _____ __________ ___ ___ __________ _______ ____.
__________ _________ ___ __________ ____ _____.
______ _____ _____ ______ ______ __________.
___ ______ __________ _______ ____ ________.
________ _________ _________ __________ ______ _______ __________.
___ ____ ___ _________ _______ _____ ______ ___ ______.
_________ ___ __________ _______ ______ ______ ________ ____ _____ _________.
______ _____ ______ ___ __________ __________ ________.
__________ ____ _______ ________ _______ ______.
___ _________ _____ __________ _____ _________ __________ ______ ______ ____ _________.
____ ________.
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