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
ECE 301 - Digital Electronics Analog Signal An analog signal is a signal that can take on a continuous range of values. Spring 2011 ECE 301 - Digital Electronics
ECE 301 - Digital Electronics Analog Signal Most, if not all, physical (naturally occurring) quantities are analog values. Time Temperature Pressure Spring 2011 ECE 301 - Digital Electronics
What is an digital signal? Spring 2011 ECE 301 - Digital Electronics
ECE 301 - Digital Electronics Digital Signal An digital signal is a signal that can take on only discrete (specific) values. Spring 2011 ECE 301 - Digital Electronics
What is an binary signal? Spring 2011 ECE 301 - Digital Electronics
ECE 301 - Digital Electronics Binary Signal An binary signal is a signal that can take on only two values. Typically represented by 0 and 1. Spring 2011 ECE 301 - Digital Electronics
Can a binary number be used to represent an analog value? What about accuracy (or is it precision)? Spring 2011 ECE 301 - Digital Electronics
Can a binary number be used to represent an digital value? How many bits are required? Spring 2011 ECE 301 - Digital Electronics
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. Sample and Hold ADC Binary Encoder analog sampled digital binary Spring 2011 ECE 301 - Digital Electronics
Basic Logic Operations Spring 2011 ECE 301 - Digital Electronics
Definition: the output is true (1) iff both inputs are true (1). AND Definition: the output is true (1) iff both inputs are true (1). logical operator F = A.B = AB = “A and B” A B A . B 1 Boolean expression F Truth table Symbol (aka. logic gate) Spring 2011 ECE 301 - Digital Electronics
ECE 301 - Digital Electronics OR Definition: the output is true (1) if either or both inputs are true (1). logical operator F = A+B = “A or B” A B A + B 1 Boolean expression F Truth table Symbol Spring 2011 ECE 301 - Digital Electronics
Definition: the output is true (1) if the input is false (0). NOT Definition: the output is true (1) if the input is false (0). logical operator F = A' = “ not A” A A' 1 Boolean expression Truth table A F = A' Symbol Spring 2011 ECE 301 - Digital Electronics
ECE 301 - Digital Electronics 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
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
Definition: the output is false (0) iff both inputs are true (1). NAND Definition: the output is false (0) iff both inputs are true (1). F = (A.B)' = “not (A and B)” A B (A . B)' 1 Boolean expression F = (A.B)' Truth table Symbol shorthand for inversion Spring 2011 ECE 301 - Digital Electronics
ECE 301 - Digital Electronics NOR Definition: the output is false (0) if either or both inputs are true (1). F = (A+B)' = “not (A or B)” A B (A+B)' 1 Boolean expression F F = (A+B)' F Truth table Symbol shorthand for inversion Spring 2011 ECE 301 - Digital Electronics
ECE 301 - Digital Electronics XOR Definition: the output is true (1) if either but not both inputs are true (1). F = A xor B A B A xor B 1 Boolean expression logical operator Truth table Symbol Spring 2011 ECE 301 - Digital Electronics
XNOR (aka. Equivalence) Definition: the output is false (0) if either but not both inputs are true (1). F = A xnor B A B A xnor B 1 Boolean expression logical operator Symbol Truth table Spring 2011 ECE 301 - Digital Electronics
ECE 301 - Digital Electronics 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 Standard Logic Gates programmable devices Read-only Memories (ROM) Programmable Logic Devices (PLD) Field Programmable Gate Arrays (FPGA) Spring 2011 ECE 301 - Digital Electronics
ECE 301 - Digital Electronics Standard Logic Gates Spring 2011 ECE 301 - Digital Electronics
ECE 301 - Digital Electronics 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
ECE 301 - Digital Electronics 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
Standard Logic Gates: 74xx08 pin-out Truth table Spring 2011 ECE 301 - Digital Electronics
Standard Logic Gates: 74xx32 pin-out Truth table Spring 2011 ECE 301 - Digital Electronics
Standard Logic Gates: 74xx04 pin-out Truth table Spring 2011 ECE 301 - Digital Electronics
Building a Logic Circuit Diagram B C A F inputs output 74xx08 74xx04 74xx32 74xx08 Boolean Expression F = B'.C + A.B Spring 2011 ECE 301 - Digital Electronics
Building a Logic Circuit V DD 7404 7408 7432 A B C F Wiring Diagram components wires inputs output Spring 2011 ECE 301 - Digital Electronics
ECE 301 - Digital Electronics Example Draw the circuit diagram and wiring diagram for the following Boolean expression: F = A'.B + A.B' Spring 2011 ECE 301 - Digital Electronics
ECE 301 - Digital Electronics Example (circuit diagram) Spring 2011 ECE 301 - Digital Electronics
ECE 301 - Digital Electronics Example Spring 2011 ECE 301 - Digital Electronics
ECE 301 - Digital Electronics Questions? Spring 2011 ECE 301 - Digital Electronics