Logic gates are the basic building blocks of any digital system. It is ?an electronic circuit that has at least one input and only one output. ?In this discussion let’s discuss logic ga

EET 130– Digital Systems I

Basic Logic Gates

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Outline of the lecture Basic Logic Functions

The Inverter

The AND gate

The OR Gate

The NAND Gate

The NOR Gate

The Exclusive OR Gate( XOR)

The Exclusive NOR Gate ( XNOR)

Fixed Function Logic Gates and Data Sheets

Objective of the Lecture  After successful completion of the lecture students

will be able to:  Describe the seven basic logic gates including their name, logic

symbol, truth table, function and Boolean expression  Determine the logic output of multiple inputs and inverted input logic

gates.  Identify pin numbers and manufacturer markings on TTL and CMOS

ICs.  Implement basic logic circuits.  Describe the operation of logic gates.  Construct truth tables and timing diagrams for logic circuits.  Identify the different fixed function logic gates  Identify the data sheet specifications for basic logic gates

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Boolean Operations

 Boolean algebra is a mathematical system for the manipulation of variables that can have one of two values.  In formal logic, these values are “true” and “false.”  In digital systems, these values are “on” and “off,” 1

and 0, or “high” and “low.”

 Boolean expressions are created by performing operations on Boolean variables.  Common Boolean operators include AND, OR, and

NOT.

Boolean Operations and Expressions

 Addition 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 1

 Multiplication 0 * 0 = 0 0 * 1 = 0 1 * 0 = 0 1 * 1 = 1

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Boolean Operations and Expressions

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 The truth table for the Boolean NOT operator is shown at the right.

 The NOT operation is most often designated by an overbar. It is sometimes indicated by a prime mark ( ‘ ) or an “elbow” (¬).

Boolean Operations and Expressions

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 A Boolean function has: • At least one Boolean variable, • At least one Boolean operator, and • At least one input from the set {0,1}.

 It produces an output that is also a member of the set {0,1}.

Now you know why the binary numbering system is so handy in digital systems

Boolean Operations and Expressions

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 A truth table describes the relationship between the input and output of a logic circuit.

 The number of entries corresponds to the number of inputs.  A 2-input table would have 22 = 4 entries.  A 3-input table would have 23 = 8 entries.

Truth Tables

Truth Tables

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Examples of truth tables with 2, 3, and 4 inputs.

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 We have looked at Boolean functions in abstract terms

 Boolean functions are implemented in digital circuits called gates

 A gate is an electronic device that produces a result based on two or more input values  In reality, gates consist of one to eight transistors, but

digital designers think of them as a single unit.  Integrated circuits contain collections of gates suited to a

particular purpose

Logic Gates

NOT Operation  The Boolean expression for the NOT operation:

“X equals NOT A” “X equals the inverse of A” “X equals the complement of A”

— Read as: X = A

A' = A

The overbar represents the NOT operation.

Another indicator for inversion is the

prime symbol (').

NOT Truth Table

The Inverter / NOT Gate

Boolean expressionTruth table 0 = LOW 1 = HIGH Pulsed waveforms

The output of an inverter is always the complement (opposite) of the input

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The NOT Gate

 Top View of a TTL 74LS family 74LS04 Hex Inverter IC Package

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1 2 3 4 5 6 7

891011121314

Ground

Vcc

AND Operations with AND gates  The AND operation is similar to multiplication:

X = A • B • C — Read as “X equals A AND B AND C”

x is true (1) when A AND B AND C are true (1)

The + sign does not stand for ordinary multiplication—it stands for the AND operation.

Truth table — Gate symbol.

The AND Gate

Boolean expression

Truth table 0 = LOW 1 = HIGH

Pulsed waveforms

The output of an AND gate is HIGH only when all inputs are HIGH

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3-Input AND Gate 4-Input AND Gate

The AND Gate

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An AND gate may have more than two inputs

The AND Gate

 Top View of a TTL 74LS family 74LS08 Quad 2-input AND Gate IC Package

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1 2 3 4 5 6 7

891011121314

Ground

Vcc

OR Operation With OR Gates

 The Boolean expression for the OR operation is: X = A + B — Read as “X equals A OR B”

The + sign does not stand for ordinary addition—it stands for the OR operation

• The OR operation is similar to addition, but when A = 1 and B = 1, the OR operation produces:

1 + 1 = 1 not 1 + 1 = 2

In the Boolean expression x = 1 + 1 + 1 = 1… x is true (1) when A is true (1) OR B is true (1) OR C is true (1)

The OR Gate

• An OR gate is a circuit with two or more inputs, whose output is equal to the OR combination of the inputs.

Truth table/circuit symbol for a two input OR gate.

The OR Gate

Boolean expression

Truth table 0 = LOW 1 = HIGH

The output of an OR gate is HIGH whenever one or more inputs are HIGH

Pulsed waveforms

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The OR Gate

3-Input OR Gate 4-Input OR Gate

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An OR gate may have more than two inputs

The OR Gate

Example of the use of an OR gate in an alarm system.

The OR Gate

 Top View of a TTL 74LS family 74LS32 Quad 2-input OR Gate IC Package

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 Another very useful gates are the exclusive OR (XOR) and exclusive NOR (XNOR) gates  The output of the XOR operation is true only when the

values of the inputs differ  The output of an XNOR operation is true only when the

inputs are the same

XOR and XNOR gates

From the above definitions can you draw the truth table for XOR and XNOR gates?

Exclusive-OR Gate

Boolean expression

Truth table 0 = LOW 1 = HIGH

The output of an XOR gate is HIGH whenever the two inputs are different

Pulsed waveforms

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Exclusive-NOR Gate

Boolean expression

Truth table 0 = LOW 1 = HIGH

The output of an XNOR gate is HIGH whenever the two inputs are identical.

Pulsed waveforms

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 NAND and NOR are two very important gates in digital systems. They are called universal gates  The output of a NAND gate is HIGH whenever one or

more inputs are LOW  The output of a NOR gate is LOW whenever one or more

inputs are HIGH

 Based on the above definitions can you draw the truth table for NAND and NOR gates?

NAND and NOR Gates

NAND and NOR Gates

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NAND and NOR universal gates

The NAND Gate • The NAND gate is an inverted AND gate.

– An inversion “bubble” is placed at the output of the AND gate, making the Boolean output expression x = AB

The NAND Gate

Boolean expression

Truth table 0 = LOW 1 = HIGH

The output of a NAND gate is HIGH whenever one or more inputs are LOW

Pulsed waveforms

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The NAND Gate

Output waveform of a NAND gate for the input waveforms shown here.

The NAND Gate

3-Input NAND Gate 4-Input NAND Gate

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A NAND gate may have more than two inputs

The NAND Gate

 Top View of a TTL 74LS family 74LS00 Quad 2-input NAND Gate IC Package

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– An inversion “bubble” is placed at the output of the OR gate, making the Boolean output expression x = A + B

The NOR Gate  The NOR gate is an inverted OR gate. 

The NOR Gate

Boolean expression

Truth table 0 = LOW 1 = HIGH

The output of a NOR gate is LOW whenever one or more inputs are HIGH.

Pulsed waveforms

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The NOR Gate

Output waveform of a NOR gate for the input waveforms shown here.

The NOR Gate

3-Input NOR Gate 4-Input NOR Gate

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A NOR gate may have more than two inputs

The NOR Gate

 Top View of a TTL 74LS family 74LS02 Quad 2-input NOR Gate IC Package

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Summary

Summary for all 2-input gates

Inputs Output of each gate

A B AND NAND OR NOR XOR XNOR

0 0 0 1 0 1 0 1

0 1 0 1 1 0 1 0

1 0 0 1 1 0 1 0

1 1 1 0 1 0 0 1

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Summary

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Basic Logic Functions

The Inverter

The AND gate

The OR Gate

The NAND Gate

The NOR Gate

The Exclusive OR Gate( XOR)

The Exclusive NOR Gate ( XNOR)

Fixed Function Logic Gates and Data Sheets