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A 3 line to 8 line decoder, with active low outputs, is used t o implement a 3- variable Boolean function as shown in the figure given below.
The simplified form of Boolean function F (A, B, C) implemented in ‘Product of Sum’ form will be
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- (X + Z). (X + Y + Z). (Y + Z)
- (X + Z). (X + Y + Z). (Y + Z)
- (X + Y + Z). (X + Y + Z). (X + Y + Z). (X + Y + Z)
- (X + Y + Z). (X + Y + Z). (X + Y + Z). (X + Y + Z)
Correct Option: B
Let us consider moment active high input F = ∑(1, 3, 5, 6)
K-map 
∴ product of sum
F = (X + Z) (Y + Z) (X + Y + Z) ...(1) for active high output
But given, signal is active low output. So each variable in equation (1) will be complemented
∴ F = (X + Z) (X + Y + Z) (Y + Z) ...(2) for active low output
