Question

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 F(x, y, z) given in the table below. y F(x, y, z) Х Z 1 1 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 0 3. Construct circuits from inverters, AND gates, and OR gates to produce the following output: a) (5 points) xy+xy b) (5 points) (x+y)(x+y)

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