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I n the given network of AND and OR gates, ƒ can be written as
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- x0 x1 x2... xn + x1 x2... xn + x2 x3... xn .... xn
- x0 x1 + x2 x3 +... + xn–1. xn
- x0 + x1 + x2 +... + xn
- x0 x1 x3... xn–1 + x2 x3 x5... xn – 1 +... + xn– 2 xn– 1 + xn
Correct Option: D
In terms of Boolean operations
Output of 1 is x0 x1
Output of 2 is (x0 x1 + x2)
Output of 3 is (x0 x1 + x2) x3 = x0 x1 x3 + x2 x3
Output of 4 is x0 x1 x3 + x2 x3 + x4
Output of 5 would be x0 x1 x3 x5 + x2 x3 x5 + x4 x5
Output of 6 would be x0 x1 x3 x5 + x2 x3 x5 + x4 x5 x6
Thus for n gates connected as shown, the output would be
x0 x1 x3 ...................... xn– 1
+ x2 x3 x5 ...................... xn– 1
+ x4 x5 x7 ...................... xn– 1
+ xh – 2 xn– 1
+ xn .
