# Boolean Algebra and Digital Logic

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Boolean Algebra and Digital Logic
Chapter 3 Boolean Algebra and Digital Logic Linda Null, Julia Lobur

Figure 03.UN01: "I've always loved that word, Boolean."
Claude Shannon

Table 03.T01: Truth Table for AND
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Table 03.T02: Truth Table for OR
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Table 03.T03: Truth Table for NOT
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Table 03.T04: The Truth Table for F(x,y,z) = x + y′z
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Table 03.T05: Basic Identities of Boolean Algebra
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Table 03.T06: Truth Table for the AND Form of DeMorgan's Law
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Table 03.T07: Truth Table Representation for a Function and Its Complement
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Table 03.T08: Truth Table Representation for the Majority Function
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Figure 03.F01: The Three Basic Gates
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Figure 03.F02: a) The Truth Table for XOR b) The Logic Symbol for XOR
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Figure 03.F03: Truth Table and Logic Symbols for NAND
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Figure 03.F04: Truth Table and Logic Symbols for NOR
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Figure 03.F05: Three Circuits Constructed Using Only NAND Gates
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Figure 03.F06: A Three-Input OR Gate Representing x + y + z

Figure 03.F07: A Three-Input AND Gate Representing x yz

Figure 03.F08: AND Gate with Two Inputs and Two Outputs
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Figure 03.F09: Logic Diagram for F(x, y, z) = x + y'z
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Figure 03.UN02: Line drawing showing a circuit.
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Figure 03.F10: Simple SSI Integrated Circuit
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Figure 03.UN08: Line drawing showing a function that evaluates to one AND gate using x and y as input. -

Table 03.T09: Truth Table for a Half-Adder

Figure 03.F11: Logic Diagram for a Half-Adder

Figure 03.F12: a) Truth Table for a Full-Adder b) Logic Diagram for a Full-Adder

Figure 03.F13: Logic Diagram for a Ripple-Carry Adder

Figure 03.F14: a) A Look Inside a Decoder b) A Decoder Symbol
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Figure 03.F15: a) A Look Inside a Multiplexer b) A Multiplexer Symbol
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Table 03.T10: Parity Generator
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Table 03.T11: Parity Checker
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Figure 03.F16: 4-Bit Shifter -

Figure 03.F17: A Simple Two-Bit ALU

Figure 03.F18: A Clock Signal Indicating Discrete Instances of Time
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Figure 03.F19: Example of Simple Feedback
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Figure 03.F20: SR Flip-Flop Logic Diagram

Figure 03.F21: a) SR Flip-Flop b) Clocked SR Flip-Flop c) Characteristic Table for the SR Flip-Flop d) Timing Diagram for the SR Flip-Flop (assuming initial state of Q is 0) -

Table 03.T12: Truth Table for SR Flip-Flop

Figure 03.F22: a) JK Flip-Flop b) JK Characteristic Table c) JK Flip-Flop as a Modified SR Flip-Flop d) Timing Diagram for JK Flip-Flop (assuming initial state of Q is 0) -

Figure 03.F23: a) D Flip-Flop b) D Flip-Flop Characteristic Table c) D Flip-Flop as a Modified SR Flip-Flop d) Timing Diagram for D Flip-Flop -

Figure 03.F24: JK Flip-Flop Represented as a Moore Machine

Figure 03.F25: Simplified Moore Machine for the JK Flip-Flop

Figure 03.F26: JK Flip-Flop Represented as a Mealy Machine

Figure 03.F27: a) Block Diagram for Moore Machines b) Block Diagram for Mealy Machines
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Figure 03.F28: Components of an Algorithmic State Machine
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Figure 03.F29: Algorithmic State Machine for a Microwave Oven
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Figure 03.UN02: Finite State Machine for Accepting a Variable Name
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Figure 03.F30: a) 4-Bit Register b) Block Diagram for a 4-Bit Register

Figure 03.F31: 4-Bit Synchronous Counter Using JK Flip-Flops

Figure 03.F32: 4 x 3 Memory -

Figure 03.F33: Convolutional Encoder for PRML
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Figure 03.F34: Stepping Through Four Clock Cycles of a Convolutional Encoder.
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Table 03.T13: Characteristic Table for the Convolutional Encoder in Figure 3.33
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Figure 03.F35: Mealy Machine for the Convolutional Encoder in Figure 3.33
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Figure 03.F36: Mealy Machine for a Convolutional Decoder
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Figure 03.F37: Trellis Diagram Illustrating State Transitions for the Sequence 00 10 11 11
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Figure 03.F38: Trellis Diagram Illustrating Hamming Errors for the Sequence 10 10 11 11
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Figure 03.AP01: Minterms for Two Variables
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Figure 03.AP02: Minterms for Three Variables
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Figure 03.AP03: Kmap for F(x,y) = x + y
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Figure 03.AP04: Groups Contain Only 1s
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Figure 03.AP05: Groups Cannot Be Diagonal
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Figure 03.AP06: Groups Must Be Powers of 2
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Figure 03.AP07: Groups Must Be as Large as Possible
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Figure 03.AP08: Minterms and Kmap Format for Three Variables
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Figure 03.AP09: Minterms and Kmap Format for Four Variables
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Figure 03.UN10: Illustration of a Kmap with 3 circled groups.
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