Representing Logic Operationspggp•Each function can be represented equivalentlyin 3 ways:equivalentlyin3ways:– Truth table–Boolean logic expressiongp– SchematicsTruth TableBoolean ExpressionSchematics5
Determining output level from a diagramgpg6
Implementing Circuits From Boolean Expressions•When the operation of a circuit is defined by a Boolean expression, we can draw a logic-circuitdiagram directly from that expression.•Example: draw the circuit fory=AC+BC+ABC•Example:drawthecircuitfor– Done in two stepsy=AC+BC+ABC7
Truth Table to Boolean Expression •List all combinations that give 1 at outputSp•Sum up all terms•Sum of products (SOP) – more laterCBACBA?=xCBAABCABCCBACBAx++=8
Laws of Boolean Algebra •Commutative LawsA + B = B + AA A ••B = B B = B ••AA•Associative LawsA + (B + C) = (A + B) + CA •(B •C) = (A •B) •C9
•Distributive LawA •(B + C) = A •B + A •CA(B+C)=AB+ACA(B+C)=AB+ACRules of Boolean Algebra10
•Rule 1OR Truth Table•Rule 2•Rule 3AND Truth Table11ANDTruthTable•Rule 4
•Rule 5OR Truth Table•Rule 6•Rule 7AND Truth Table12•Rule 8
Answers
Answer:
Representing Logic Operationspggp•Each function can be represented equivalentlyin 3 ways:equivalentlyin3ways:– Truth table–Boolean logic expressiongp– SchematicsTruth TableBoolean ExpressionSchematics5
Determining output level from a diagramgpg6
Implementing Circuits From Boolean Expressions•When the operation of a circuit is defined by a Boolean expression, we can draw a logic-circuitdiagram directly from that expression.•Example: draw the circuit fory=AC+BC+ABC•Example:drawthecircuitfor– Done in two stepsy=AC+BC+ABC7
Truth Table to Boolean Expression •List all combinations that give 1 at outputSp•Sum up all terms•Sum of products (SOP) – more laterCBACBA?=xCBAABCABCCBACBAx++=8
Laws of Boolean Algebra •Commutative LawsA + B = B + AA A ••B = B B = B ••AA•Associative LawsA + (B + C) = (A + B) + CA •(B •C) = (A •B) •C9
•Distributive LawA •(B + C) = A •B + A •CA(B+C)=AB+ACA(B+C)=AB+ACRules of Boolean Algebra10
•Rule 1OR Truth Table•Rule 2•Rule 3AND Truth Table11ANDTruthTable•Rule 4
•Rule 5OR Truth Table•Rule 6•Rule 7AND Truth Table12•Rule 8
Answer:
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