combinational logic digital design department of software development faculty of information...
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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
Dr. Rebhi BarakaDr. Rebhi Baraka
Basic Combinational Logic CircuitsBasic Combinational Logic Circuits
• AND-OR LogicAND-OR Logic• AND-OR-Invert LogicAND-OR-Invert Logic• Exclusive-OR LogicExclusive-OR Logic
Basic Combinational Logic CircuitsBasic Combinational Logic Circuits
• AND-OR LogicAND-OR Logic
Basic Combinational Logic CircuitsBasic Combinational Logic Circuits
• AND-OR Invert LogicAND-OR Invert Logic
Basic Combinational Logic CircuitsBasic Combinational Logic Circuits
• Exclusive-OR LogicExclusive-OR Logic
Basic Combinational Logic CircuitsBasic Combinational Logic Circuits
• Exclusive-NOR LogicExclusive-NOR Logic
Implementing Combinational LogicImplementing Combinational Logic
• 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.
Implementing Combinational LogicImplementing Combinational Logic
• From Boolean expression to logic circuitFrom Boolean expression to logic circuit
Logic circuit for Logic circuit for XX = = ABAB + + CDECDE . .
Implementing Combinational LogicImplementing Combinational Logic
• Implement the following Boolean expression:Implement the following Boolean expression:
Implementing Combinational LogicImplementing Combinational Logic
• 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
Implementing Combinational LogicImplementing Combinational Logic
• From truth table to logic circuit (continued)From truth table to logic circuit (continued)
Implementing Combinational LogicImplementing Combinational Logic
• 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
Input Output
A B C X
00001111
00110011
01010101
00010110
A’BC
AB’CABC’
Implementing Combinational LogicImplementing Combinational Logic
• 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