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Chapter 4 Logic Gates and Boolean Algebra

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Introduction Logic gates are the actual physical implementations of the logical operators. These gates form the basic building blocks for all digital logic circuits. Logic gates process signals which represent true or false.

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Introduction Gates are identified by their function: NOT, AND, NAND, OR, NOR, EX-OR and EX- NOR. Switch S1 OR Switch S2 (or both of them) must be closed to light the lamp Switch S1 AND Switch S2 must be closed to light the lamp

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Truth Table A truth table is a means for describing how a logic circuit's output depends on the logic levels present at the circuit's inputs.

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Logic Gates and Circuit Diagrams OR Gate

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Logic Gates and Circuit Diagrams AND Gate AND Gate

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Logic Gates and Circuit Diagrams NOT Gate

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Logic Gates and Circuit Diagrams NOR Gate

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Logic Gates and Circuit Diagrams NAND Gate

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Logic Gates and Circuit Diagrams EX-OR gate The 'Exclusive-OR' gate is a circuit which will give a high output if either but not both, of its two inputs are high. EX-NOR gate is The inversion of EX-OR Gate

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Describing Logic Circuits Algebraically

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Evaluating Logic Circuit Outputs

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Determining Output Level from a Diagram

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Implementing Circuits From Boolean Expression

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Boolean Algebra Simplification of logical circuits. One tool to reduce logical expressions is the mathematics of logical expressions. The rules of Boolean Algebra are simple and straight-forward, and can be applied to any logical expression.

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Boolean Algebra

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AB(A + B ’ C +C) Solution: ABA + ABB ’ C + ABC AB + 0 + ABC AB + ABC AB (A ’ B) ’ (A+B) Solution: (A + B ’ ) (A + B) AA + B ’ A + AB + B ’ B A + B ’ A + AB A + AB A

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Boolean Algebra

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Universality of NAND & NOR Gates

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Alternate Logic Gate Representations

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Forms and Definitions of Boolean Expressions

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Product of Sums Representation

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Disjunctive Normal Form

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Using truth tables, convert this expression into a sum of minterms

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