# Logic gates are the basic building blocks of any digital sys…

Logic gates are the basic building blocks of any digital sys…

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 gates and how the combination of  these logic gates can be used to implement the functioning of real-world  applications.

Is the NOR gate a universal gate?
What does an invert bubble at the input of a logic gate mean? (Hint: Active High or Low)
Consider the following statement “A car alarm will sound if the door is open or the window is open”

Translate that statement into a logic diagram. Use ‘A’ as the input from the car door and ‘B’ as the input from the car window.

Can you think of other statements that can be translated to logic circuits?
Discuss the statement “Translating logical statements into logic circuits.”

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

EET 130– Digital Systems I
Outline of the lecture
Objective of the Lecture
Boolean Operations
Boolean Operations and Expressions
Boolean Operations and Expressions
Slide Number 7
Boolean Operations and Expressions
Truth Tables
Truth Tables
Logic Gates
NOT Operation
The Inverter / NOT Gate
The NOT Gate
AND Operations with AND gates
The AND Gate
The AND Gate
The AND Gate
OR Operation With OR Gates
The OR Gate
The OR Gate
The OR Gate
Slide Number 23
The OR Gate
XOR and XNOR gates
Exclusive-OR Gate
Exclusive-NOR Gate
NAND and NOR Gates
NAND and NOR Gates
The NAND Gate
The NAND Gate
The NAND Gate
The NAND Gate
The NAND Gate
The NOR Gate
The NOR Gate
The NOR Gate
The NOR Gate
The NOR Gate
Summary
Summary

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