Simplified expression of Y = ( A + B )( A + overline A overline B )C + overline A ( B + overline C ) + overline A B + ABC is

Y = C( A + B ) + overline A ( B + overline C )

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This question belongs to Electronics And Communications Engineering Digital Electronics

Digital Electronics

Simplified expression of $${\text{Y}} = \left( {{\text{A}} + {\text{B}}} \right)\left( {{\text{A}} + \overline {\text{A}} \overline {\text{B}} } \right){\text{C}} + \overline {\text{A}} \left( {{\text{B}} + \overline {\text{C}} } \right) + \overline {\text{A}} {\text{B}} + {\text{ABC}}$$ is

A) $${\text{Y}} = {\text{C}}\left( {{\text{A + B}}} \right) + \overline {\text{A}} \left( {{\text{B}} + \overline {\text{C}} } \right)$$ B) $${\text{Y}} = {\text{C}}\left( {\overline {\text{A}} + \overline {\text{B}} } \right) + {\text{A}}\left( {\overline {\text{B}} + {\text{C}}} \right)$$ C) $${\text{Y}} = {\text{A}}\left( {{\text{B}} + {\text{C}}} \right) + {\text{B}}\left( {\overline {\text{A}} + \overline {\text{C}} } \right)$$ D) $${\text{Y}} = {\text{C}}\left( {\overline {\text{A}} + {\text{B}}} \right) + {\text{B}}\left( {{\text{A}} + \overline {\text{C}} } \right)$$

Answer & Solution

Correct Answer: Option A

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Simplified expression of $${\text{Y}} = \left( {{\text{A}} + {\text{B}}} \right)\left( {{\text{A}} + \overline {\text{A}} \overline {\text{B}} } \right){\text{C}} + \overline {\text{A}} \left( {{\text{B}} + \overline {\text{C}} } \right) + \overline {\text{A}} {\text{B}} + {\text{ABC}}$$ is

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