Exam 12: A: Boolean Algebra

Write $( x + y z ) ( \bar { x } + y z )$ as a sum-of-products in the variables x, y, and z.

$\text { Let } F ( x , y , z ) = \overline { ( \bar { y } z ) } ( x + \bar { x } y ) \text {. }$ Draw a logic gate diagram for F .

Draw a logic gate diagram for the Boolean function $F ( x , y , z ) = ( x \bar { y } ) + x \bar { z }$

determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables. - $( 0 + x ) ( 1 + x ) = x x$

Using only the five properties associative laws, commutative laws, distributive laws, identity laws, and com- plement laws, prove that x + x = x is true in all Boolean algebras.

fill in the blanks. -There are ____ Boolean functions with 2 variables.

Write 1 as a sum-of-products in the variables x and y.

If $f ( w , x , y , z )$ = $\overline { ( \bar { x } + y \bar { z } ) }$ + $( \bar { w } x )$ , find $f ( 1,1,0,0 )$

Using only the five properties associative laws, commutative laws, distributive laws, identity laws, and com- plement laws, prove that x + (x y) = x is true in all Boolean algebras.

determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables. - $x + x y z = x$

Using only the five properties associative laws, commutative laws, distributive laws, identity laws, and com- plement laws, prove that x + 1 = 1 is true in all Boolean algebras.

determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables. - $x + x \bar { y } = x y z + x ( \bar { z } + \bar { y } z )$

determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables. - $( x x + 1 ) = ( x + 1 ) ( x + 1 )$

If $f ( w , x , y , z )$ = $\overline{( \bar { x } + y \bar { z } )}$ + $( \bar { w } x )$ , find $f$ (0,1,0,1) .

determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables. - $\overline { x + y } = \bar { x } + \bar { y }$

fill in the blanks. -The idempotent laws in a Boolean algebra state that ____ and ____.

If $f ( w , x , y , z )$ = $\overline{( \bar { x } + y \bar { z } )}$ + $( \bar { w } x )$ , find $f$ (0,0,1,0).

Find the sum-of-products expansion of the Boolean function f(x, y) that is 1 if and only if either x = 0 and $y = 1 \text {, or } x = 1 \text { and } y = 0$

determine whether the statement is TRUE or FALSE. Assume that x, y, and z represent Boolean variables. - $\overline { y z + \bar { x } } = \overline { y z } x$

Use the Quine-McCluskey method to simplify the Boolean expression $w x y z + w x y \bar { z } + w \bar { x } y z + w \bar { x } y \bar { z } +$ $\bar { w } \bar { x } y z + w \bar { x } \bar { y } z + \bar { w } \bar { x } \bar { y } z$