Why cascaded inverters are used in the multiplexer when it is possible to realize the circuit using a single inverter.
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The front inverters are used to buffer the input signal. Without the front inverters inputs A and B would be 3 load units each instead of 1, since you would have to drive both the rear inverters as well as both of the and gates used with the input's term in the multiplexer logic.

Ignacio Vazquez-Abrams
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front inverters means inverters on the right side ? – tollin jose Apr 01 '14 at 06:12
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On the left side. The ones on the right side are used for logic purposes. – Ignacio Vazquez-Abrams Apr 01 '14 at 06:12
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"Without the front inverters inputs A and B would be 3 load units each instead of 1." Can you please elaborate this point ? – tollin jose Apr 01 '14 at 06:15
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@tollin: Updated. – Ignacio Vazquez-Abrams Apr 01 '14 at 06:17
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@IgnacioVazquez-Abrams please make it more clear..? – BASIL VARGHESE Apr 01 '14 at 10:02
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@BASILVARGHESE: Which part is unclear? – Ignacio Vazquez-Abrams Apr 01 '14 at 10:12
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"Without the front inverters inputs A and B would be 3 load units each instead of 1" In this you meant 3 loads as AND Gates??? @IgnacioVazquez-Abrams – BASIL VARGHESE Apr 02 '14 at 06:10
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@BASILVARGHESE: As the answer explains, one of the loads is the other inverter and the other two are and gates. The 2-input multiplexer equation uses each of the non-inverted inputs twice. – Ignacio Vazquez-Abrams Apr 02 '14 at 11:47