LN3-digitalLogic_ans

LN3-digitalLogic_ans - 1. Simplify the following...

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Unformatted text preview: 1. Simplify the following expressions using Boolean algebra identities. a. F ( x , y , z ) = x y + xy z + xyz i. ii. iii. iv. v. vi. = x y + xy ( z + z ) => Distributive law = x y + xy (1) => Inverse law = x y + xy => Identity law = ( x + x) y => Distributive law = (1) y => Inverse law =y => Identity law b. F ( x , y , z ) = ( x + y ) ( x + y ) i. = ( x + y )( x. y ) ii. iii. iv. v. vi. = ( x + y )( xy ) = ( x y )( xy) = ( x x)( y y ) = 0.0 =0 => DeMorgan’s law => Double complement => DeMorgan’s law => Associative Law => Inverse => Idempotent 2. The truth table for a Boolean expression is shown here. a. Write the expression in: * Sum-of-products form. F = x yz + x yz + xyz * Product-of-sums form. x yz + x yz + xy z + xyz + xyz ( x y z )( x yz )( xy z )( xyz )( xyz) X 0 0 0 0 1 1 1 1 Y 0 0 1 1 0 0 1 1 Z 0 1 0 1 0 1 0 1 F 1 0 0 1 0 0 1 0 F = ( x + y + z )( x + y + z )( x + y + z )( x + y + z )( x + y + z ) b. Draw a circuit to implement the truth table. Page 1 of 1 ...
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