Combinational Logic Combinational Logic Digital Design Digital Design Department of Software Development Department of Software Development Faculty of Information Technology Faculty of Information Technology Islamic University of Gaza Islamic University of Gaza Dr. Rebhi Baraka Dr. Rebhi Baraka [email protected]
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Combinational Logic Digital Design Department of Software Development Faculty of Information Technology Islamic University of Gaza Dr. Rebhi Baraka [email protected].
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Combinational LogicCombinational Logic
Digital DesignDigital Design
Department of Software DevelopmentDepartment of Software Development
Faculty of Information TechnologyFaculty of Information Technology
Islamic University of GazaIslamic University of Gaza
• From Boolean expression to logic From Boolean expression to logic circuitcircuit– Given a Boolean expression, create a Given a Boolean expression, create a
logic circuit that implements that logic circuit that implements that expression.expression.
• From truth table to logic circuitFrom truth table to logic circuit– Given a truth table, create a logic circuit Given a truth table, create a logic circuit
that implements that table.that implements that table.
• From truth table to logic circuitFrom truth table to logic circuit– Given a truth table, create a logic circuit that Given a truth table, create a logic circuit that
implements that table.implements that table.Input Output
A B C X
00001111
00110011
01010101
00011000
A’BCAB’C’
The SOP expression obtained from the truth table is
• Example: Design a logic circuit to implement the operation specified in the truth tableExample: Design a logic circuit to implement the operation specified in the truth table
• Example: Design a logic circuit with 4 inputs that will only produce a 1 output when exactly Example: Design a logic circuit with 4 inputs that will only produce a 1 output when exactly 3 inputs are 1s.3 inputs are 1s.
The combinations in which there are exactly 3 1s are listed in the table with their product termsThe combinations in which there are exactly 3 1s are listed in the table with their product terms
A B C D
0111
1011
1101
1110
A’BCDAB’CDABC’DABCD’
X = A’BCD + AB’CD + ABC’D + ABCD’
The Universal Property The Universal Property of NAND and NOR Gatesof NAND and NOR Gates
NAND and NOR gates are “universal” because they can be NAND and NOR gates are “universal” because they can be used to produce any of the other logic functions.used to produce any of the other logic functions.
The Universal Property of NAND GatesThe Universal Property of NAND Gates
The Universal Property of NOR GatesThe Universal Property of NOR Gates
These slides are based on Digital Fundamentals 9These slides are based on Digital Fundamentals 9 thth ed. By Thomas Floyd ed. By Thomas Floyd