# ECE 331 - Digital System Design ECE 331 Digital System Design Basic Logic Operations and Standard Logic Gates (Lecture #1) What is an analog signal? Spring 2011 ECE 301 - Digital Electronics 2 Analog Signal An analog signal is a signal that can take on a continuous range of values. Spring 2011

ECE 301 - Digital Electronics 3 Analog Signal Most, if not all, physical (naturally occurring) quantities are analog values. Spring 2011 Time Temperature Pressure

ECE 301 - Digital Electronics 4 What is an digital signal? Spring 2011 ECE 301 - Digital Electronics 5 Digital Signal An digital signal is a signal that can take on only discrete (specific) values. Spring 2011 ECE 301 - Digital Electronics

6 What is an binary signal? Spring 2011 ECE 301 - Digital Electronics 7 Binary Signal An binary signal is a signal that can take on only two values. Spring 2011 Typically represented by 0 and 1. ECE 301 - Digital Electronics

8 Can a binary number be used to represent an analog value? What about accuracy (or is it precision)? Spring 2011 ECE 301 - Digital Electronics 9 Can a binary number be used to represent an digital value? How many bits are required? Spring 2011 ECE 301 - Digital Electronics 10 Processing Physical Quantities

The analog signal (representing the physical quantity) must be sampled at specific instances in time. The sampled values must be digitized. The digital value must be encoded in binary. analog Spring 2011 Sample and Hold sampled

ADC digital ECE 301 - Digital Electronics Binary Encoder binary 11 Basic Logic Operations Spring 2011 ECE 301 - Digital Electronics 12 AND Definition: the output is true (1) iff both inputs

are true (1). logical operator F = A.B = AB = A and B Boolean expression F A B A.B 0 0 0 0 1

0 1 0 0 1 1 1 Truth table Symbol (aka. logic gate) Spring 2011 ECE 301 - Digital Electronics 13

OR Definition: the output is true (1) if either or both inputs are true (1). logical operator F = A+B = A or B Boolean expression FF A B A+B 0 0 0

0 1 1 1 0 1 1 1 1 Truth table Symbol Spring 2011

ECE 301 - Digital Electronics 14 NOT Definition: the output is true (1) if the input is false (0). logical operator F = A' = not A A A' Boolean expression 0 1 1

0 Truth table A F = A' Symbol Spring 2011 ECE 301 - Digital Electronics 15 Order of Precedence The order of precedence of the basic logic operations is defined as follows:

NOT AND OR The order of precedence can be modified by using parenthesis. Spring 2011 ECE 301 - Digital Electronics 16 Functionally Complete

The AND, OR, and NOT operations comprise a functionally complete set. All logic functions can be expressed in terms of these logic operations. All logic circuits can be realized using the associated logic gates. Spring 2011 ECE 301 - Digital Electronics 17 NAND Definition: the output is false (0) iff both inputs are true (1). F = (A.B)' = not (A and B) Boolean expression

F = (A.B)' A B (A . B)' 0 0 1 0 1 1 1 0

1 1 1 0 Truth table Symbol Spring 2011 shorthand for inversion ECE 301 - Digital Electronics 18 NOR Definition: the output is false (0) if either or both inputs are true (1). F = (A+B)' = not (A or B) Boolean expression

FFFF= (A+B)' Symbol Spring 2011 A B (A+B)' 0 0 1 0 1 0

1 0 0 1 1 0 Truth table shorthand for inversion ECE 301 - Digital Electronics 19 XOR Definition: the output is true (1) if either but not both inputs are true (1). F = A xor B

Boolean expression logical operator A B A xor B 0 0 0 0 1 1 1

0 1 1 1 Truth table 0 Symbol Spring 2011 ECE 301 - Digital Electronics 20 XNOR (aka. Equivalence) Definition: the output is false (0) if either but not both inputs are true (1). F = A xnor B

Boolean expression logical operator Symbol Spring 2011 A B A xnor B 0 0 1 0 1

0 1 0 0 1 1 1 Truth table ECE 301 - Digital Electronics 21 Logic Circuits

Logic circuits are realized through the interconnection of logic gates. Each logic gate represents a logical operation. This can be done using discrete components programmable devices Spring 2011

Standard Logic Gates Read-only Memories (ROM) Programmable Logic Devices (PLD) Field Programmable Gate Arrays (FPGA) ECE 301 - Digital Electronics 22 Standard Logic Gates Spring 2011 ECE 301 - Digital Electronics 23 Standard Logic Gates Device Logic Gate 74xx08

Quad 2-input AND gate 74xx32 Quad 2-input OR gate 74xx04 Hex Inverter (NOT gate) 74xx00 Quad 2-input NAND gate 74xx02 Quad 2-input NOR gate 74xx86 Quad 2-input XOR gate Note: xx refers to the logic family

Spring 2011 ECE 301 - Digital Electronics 24 Standard Logic Gates 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. Spring 2011 ECE 301 - Digital Electronics

25 Standard Logic Gates: 74xx08 pin-out Truth table Spring 2011 ECE 301 - Digital Electronics 26 Standard Logic Gates: 74xx32 pin-out Truth table Spring 2011 ECE 301 - Digital Electronics

27 Standard Logic Gates: 74xx04 pin-out Truth table Spring 2011 ECE 301 - Digital Electronics 28 Building a Logic Circuit Circuit Diagram C 74xx08 B 74xx04

inputs 74xx32 A output 74xx08 F = B'.C + A.B Spring 2011 F ECE 301 - Digital Electronics Boolean Expression 29

Building a Logic Circuit VDD Wiring Diagram components 7404 wires 7408 inputs Spring 2011 A B C 7432 F output

ECE 301 - Digital Electronics 30 Example Draw the circuit diagram and wiring diagram for the following Boolean expression: F = A'.B + A.B' Spring 2011 ECE 301 - Digital Electronics 31 Example (circuit diagram) Spring 2011 ECE 301 - Digital Electronics

32 Example Spring 2011 ECE 301 - Digital Electronics 33 Questions? Spring 2011 ECE 301 - Digital Electronics 34