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ECE 331 – Digital System Design
Basic Logic Functions,Truth Tables,
andStandard Logic Gates
ECE 331 - Digital System Design 2
Basic Logic Functions
ECE 331 - Digital System Design 3
Basic Logic Functions
AND Logical multiplication (product) A . B = AB = “A and B”
OR Logical addition (sum) A + B = “A or B”
NOT Logical complement A‘ = “not A”
Order of Precedence:1. NOT2. AND3. OR- can be modified by parenthesis
ECE 331 - Digital System Design 4
Truth Table
ECE 331 - Digital System Design 5
x 1 x 2
x n
x 1 x 2 x n + + + x 1 x 2
x 1 x 2 +
x 1 x 2
x n
x 1 x 2
x 1 x 2 x 1 x 2 x n
(a) AND gates
(b) OR gates
x x
(c) NOT gate
Logic Gates
ECE 331 - Digital System Design 6
Additional Logic Functions NAND
F = (A . B)‘ = (AB)’ F = not (A and B) Compound logic function
NOR F = (A + B)’ F = not (A or B) Compound logic function
Not the same as F = A’ . B’
Not the same as F = A’ + B’
ECE 331 - Digital System Design 7
Truth Tables
Exercise:
Derive the Truth Table for the NAND and NOR gates.
ECE 331 - Digital System Design 8
x 1 x 2
x n
x 1 x 2 x n + + + x 1 x 2
x 1 x 2 +
x 1 x 2
x n
x 1 x 2
x 1 x 2 x 1 x 2 x n
(a) NAND gates
(b) NOR gates
Logic Gates
shorthand for a NOT gate
ECE 331 - Digital System Design 9
Additional Logic Functions
Exclusive-OR F = (A.B') + (A'.B) Output = 1 iff one of the inputs is 1 (but not both). Inclusive-OR: F = A + B
Exclusive-NOR F = (A.B) + (A'.B') Output = 1 iff both input are 0 or both inputs are
1. Also known as the Equivalence function.
ECE 331 - Digital System Design 10
Truth Tables
Exercise:
Derive the Truth Table for the XOR and XNOR gates.
ECE 331 - Digital System Design 11
Additional Logic Operations
XOR gate
XNOR gate
A B
F = A xor B
F = A xnor B
ECE 331 - Digital System Design 12
Truth Tables
ECE 331 - Digital System Design 13
Truth Tables Used to describe the functional behavior of a Boolean
expression and/or Logic circuit. Each row in the truth table represents a unique
combination of the input variables. For n input variables, there are 2n rows.
The output of the logic function is defined for each row. Each row is assigned a numerical value, with the rows
listed in ascending order. The order of the input variables defined in the logic
function is important.
ECE 331 - Digital System Design 14
3-input Truth Table
ECE 331 - Digital System Design 15
4-input Truth Table
ECE 331 - Digital System Design 16
Standard Logic Gates
ECE 331 - Digital System Design 17
Standard Logic Gates
Discrete components used to build logic circuits. 74xx08 AND gate 74xx32 OR gate 74xx04 NOT gate 74xx00 NAND gate 74xx02 NOR gate 74xx86 XOR gate
Logic Families (TTL, LS-TTL, F, HC)
ECE 331 - Digital System Design 18
Standard Logic Gates: Data sheets
Data sheets provide essential information: Logic Function Truth Table Pin-out Electrical Characteristics Timing Characteristics Package Description(s)
This information is necessary when building logic circuits from discrete components.
Each Logic Family has a unique set of characteristics.
ECE 331 - Digital System Design 19
Logic Families TTL
Low-Power TTL (“L”) High-Speed TTL (“H”) Schottky (“S”) Low-Power Schottky (“LS”) Advanced Schottky (“AS”) Advanced Low-Power Schottky (“ALS”) Fast (“F”)
CMOS High-Speed CMOS (“HC”) Advanced CMOS (“AC”)
ECE 331 - Digital System Design 20
Table E.4 (p. 916 of textbook)
ECE 331 - Digital System Design 21
Combinational Logic Circuits
ECE 331 - Digital System Design 22
Combinational Logic Circuits
Composed of an interconnected set of logic gates. Also known as Switching Circuits Logic circuits can be designed from
Truth tables Boolean expressions
Logic circuits realized through Interconnection of discrete components Synthesis from a Hardware Description Language
ECE 331 - Digital System Design 23
Example:
Derive the Boolean expression and draw the circuit diagram for the following truth table:
ECE 331 - Digital System Design 24
f
x 1
x 2
Example
F = x’1.x’
2 + x’
1.x
2 + x
1.x
2
ECE 331 - Digital System Design 25
Example:
Derive the Boolean expression and draw the circuit diagram for the following truth table:
ECE 331 - Digital System Design 26
Wiring Diagrams
ECE 331 - Digital System Design 27
(a) Dual-inline package
(b) Structure of 7404 chip
V DD
Gnd
Standard Logic Gate: Pin-out
ECE 331 - Digital System Design 28
Standard Logic Gate: Pin-out
ECE 331 - Digital System Design 29
Standard Logic Gate: Pin-out
ECE 331 - Digital System Design 30
Example:
Draw the circuit diagram and the wiring diagram for the following Boolean expression:
F = x’2.x
3 + x
1.x
2
ECE 331 - Digital System Design 31
V DD
x 1 x 2 x 3
f
7404
7408 7432
Example