Chapter 3Describing Logic Circuits

Boolean Variables Boolean variables : ‘0’ or ‘1’

Logic 0 Logic 1False TrueOff OnLow HighNo YesOpen switch Closed switch

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Boolean Algebra Boolean algebra : expressing the

relationship between a logic circuit’s inputs and outputs

Three basic operation : OR(+), AND(・), NOT( ￣ )

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Truth Tables Truth table : describing how a logic circuit’s

output depends on the logic levels present at the circuit’s inputs

Number of output combinations will equal 2N for an N-input truth table

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

OR Operation with OR Gates The Boolean expression for the OR

operations is

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Example 3-1

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Example 3-2

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

AND Operation with AND Gates The Boolean expression for the AND

operations is

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Example 3-9

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

NOT Operation The Boolean expression for NOT

Operation is

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Summery of Boolean Operations

OR AND NOT0 + 0 = 0 0 ・ 0 = 0 0 = 10 + 1 = 1 0 ・ 1 = 0 1 = 01 + 0 = 1 1 ・ 0 = 01 + 1 = 1 1 ・ 1 = 1

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Describing Logic Circuits Algebraically

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Circuits Containing INVERTERs

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Evaluating Logic-Circuit Outputs

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Evaluating Logic-Circuit Outputs A=0, B=1, C=1, D=1 A=0, B=0, C=1, D=1, E=1

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Evaluating a Boolean expression Perform all inversions of single terms Perform all operations within parentheses Perform an AND operation before an OR

operation If an expression has a bar over it, perform the

operations inside the expression first and then invert the result

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Determining Output Level from a Diagram

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Implementing Circuits from Boolean Expressions

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

NOR Gate The output

expression for NOR gate is

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Example 3-8

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

NAND Gate The output expression for NAND gate is

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Example 3-10

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Boolean Theorems

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

AND

OR

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Multivariable TheoremsCommutative laws

Associative laws

Distributive laws

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

DeMorgan’s Theorems

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Implications of DeMorgan’s Theorems

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Implications of DeMorgan’s Theorems (cont.)

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Universality of NAND Gates

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Universality of NOR Gates

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Example 3-18

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Alternate Logic-Gate Representations

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits

Logic-Symbol Interpretation

INC222 Logic Theory and Digital Circuit Design Chapter 3 Describing Logic Circuits