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Q. Logic diagrams for same Boolean expression?
The expression F can be simplified using Boolean algebra.
The logic diagram of simplified expression is drawn in fig (b) below using NOT, OR and AND gates (the same operation can be done by employing a single XOR gate). So the number of gates are decreased to 5 gates (2 inverters, 2 AND gates & 1 OR) in place of 7 gates. (3 inverters, 3 AND & 1 OR gate).
Algebraic function can emerge in several different forms though a process of simplification exists however it is awkward due to absence of routes that tell what rule to apply next. The Karnaugh map is a simple direct technique of simplification of logic expressions.
Q. Can a vector have a component equivalent to zero and still have a nonzero magnitude? Answer:- Yes For example the 2-dimensional vector (1, 0) has length sqrt (1+0) = 1
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