Question

If Y = ABC + BCbarD + AbarBC then simplify the equation and realize using basic gates and also
realize the simplified equation using only NOR gates.

Answer 1

Given : Y = ABC + BCbarD + AbarBC

$Y = ABC + B\overline{C}D+\overline{A}BC$

To Find :  Simplify

Solution:

$Y = ABC + B\overline{C}D+\overline{A}BC$

Rearrange terms

$\implies Y = ABC +\overline{A}BC+ B\overline{C}D$

Take BC common

$\implies Y = BC(A +\overline{A})+ B\overline{C}D$

$(A +\overline{A})= 1$

$\implies Y = BC(1)+ B\overline{C}D$

$\implies Y = BC + B\overline{C}D$

Take B common

$\implies Y = B(C + \overline{C}D)$

B = 0  => Y = 0

If B =  1  

then  C = 1   => Y = 1

C = 0  and  D = 0  => Y = 0

C = 0  and D = 1  => Y = 1

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