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1. (5 points) Find the output of the given circuit: x х Db 2. (5 points) Find the sum-of-products expansion for the function
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Answer #1

1.

Let the circuit be labelled as follows :

х A D Y с D х B I Y

A = X Y

B = X ' + Y

C = ( ( X ' + Y ) ( X Y ) ) '

Applying De Morgan's law :

C = ( X ' + Y ) ' +  ( X Y ) '

Applying De Morgan's law :

C = X Y ' + ( X ' + Y ' )

C = X ' + Y ' + Y ' [ Absorption law ]

C = X ' + Y ' [ Idempotent law ]

So, the output of the given circuit is :

X ' + Y ' .

2.

The sum of product expression from the given truth table is :

F ( x, y, z ) = Σ ( 2, 4, 7 )

= x ' y ' z ' + x y ' z ' + x y z

3.

a)

The expression given is :

( xy ) ' + x ' y '

The circuit for the given expression is :

х y D

b)

The expression given is :

( x + y ) ' ( x ' + y )

The circuit for the given expression is :

х у

  

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