Introduction. BME208 Logic Circuits Yalçın İŞLER

Transcription

1 Introduction BME208 Logic Circuits Yalçın İŞLER 1

2 Lecture Three hours a week (three credits) No other sections, please register this section Tuesday: 09:30 12:15 (BME-LAB #2) Attendance is compulsory 2

3 Laboratory Three sections Check from the department website 7 experiments Once in two weeks It is obligatory to do all the assignments See assistants for grading scheme Work in groups of two 3

4 Grading One midterm exam Weight: 40% November 11, 2015 (Not determined yet) Final exam Weight: 40% As scheduled by the registration office Homeworks & Project Weight: 20% You need to learn Verilog HDL 4

5 Lab Assistants Özlem Karabiber 5

6 Yalçın İŞLER Contact Information Place: Central Offices #1, 2nd Floor, Room yahoo.com Office hours: Whenever you find me Or by appointment 6

7 Motivation Analysis & design of digital electronic circuits Why digital circuits? They are everywhere and generic digital computers, smart phones, data communication, digital recording, digital TV, many others Fundamental concepts in the design of digital systems Basic tools for the design of digital circuits Logic gates (AND, OR, NOT) Boolean algebra 7

8 What is a Digital System? One characteristic: Ability of manipulating discrete elements of information A set that has a finite number of elements contains discrete information Examples for discrete sets Decimal digits {0, 1,, 9} Alphabet {A, B,, Y, Z} Binary digits {0, 1} One important problem how to represent the elements of discrete sets in physical systems? 8

9 How to Represent? In electronics circuits, we have electrical signals voltage current Different strengths of a physical signal can be used to represent elements of the discrete set. Which discrete set? Binary set is the easiest two elements {0, 1} Just two signal levels: 0 V and 5 V This is why we use binary system to represent the information in digital systems. 9

10 How to Represent? In electronics circuits, we have electrical signals voltage current Base current 4.5 μa Collector current 4.5mA +5V 1k 1M F = V or 0V 0V 10

11 Binary System Binary set {0, 1} The elements of binary set, 0 and 1 are called binary digits or shortly bits. How to represent the elements of other discrete sets Decimal digits {0, 1,, 9} Alphabet {A, B,, Y, Z} Elements of any discrete set can be represented using groups of bits A

12 How Many Bits? What is the formulae for number of bits to represent a discrete set of n elements {0, 1, 2, 3} 00 0, 01 1, 10 2, and {0, 1, 2, 3, 4, 5, 6, 7} 000 0, 001 1, 010 2, ands , 101 5, 110 6, ands The formulae, then, #of bits required= log 2 #of Symbols If n = 9, then? bits are needed 12

13 Nature of Information Is information of discrete nature? Sometimes, but usually not. Anything related to money (e.g. financial computations, accounting etc) involves discrete information In nature, information comes in a continuous form temperature, humidity level, air pressure, etc. Continuous data must be converted (i.e. quantized) into discrete data lost of some of the information We need ADC (DAC) 13

14 General-Purpose Computers Best known example for digital systems Components CPU, I/O units, Memory unit CPU Memory I/O Registers Inter connect ALU Control Outside world FPU Multiplier/ CPU Divider General-purpose computer 14

15 Textbook & References Textbook M. Morris ManoDigital Design: With an Introduction to the Verilog HDL, 5th Edition, Prentice Hall, Other references Tens of digital design books Lectures from MIT Open Courseware and Stanford 15

16 Contents 1 Digital Systems and Binary Numbers Digital Systems Binary Numbers Number Base Conversions Octal and Hexadecimal Numbers Complements of Numbers Signed Binary Numbers Binary Codes Binary Storage and Registers Binary Logic 30 16

17 Contents 2 Boolean Algebra and Logic Gates Introduction Basic Definitions Axiomatic Definition of Boolean Algebra Basic Theorems and Properties of Boolean Algebra Boolean Functions Canonical and Standard Forms Other Logic Operations Digital Logic Gates Integrated Circuits 66 17

18 Contents 3 Gate Level Minimization Introduction The Map Method Four Variable K-Map Product of Sums Simplification Don t Care Conditions NAND and NOR Implementation Other Two Level Implementations Exclusive OR Function Hardware Description Language

19 Contents 4 Combinational Logic Introduction Combinational Circuits Analysis Procedure Design Procedure Binary Adder Subtractor Decimal Adder Binary Multiplier Magnitude Comparator Decoders Encoders Multiplexers HDL Models of Combinational Circuits

20 Contents 5 Synchronous Sequential Logic Introduction Sequential Circuits Storage Elements: Latches Storage Elements: Flip Flops Analysis of Clocked Sequential Circuits Synthesizable HDL Models of Sequential Circuits State Reduction and Assignment Design Procedure

21 Contents 6 Registers and Counters Registers Shift Registers Ripple Counters Synchronous Counters Other Counters HDL for Registers and Counters

22 Contents 7 Memory and Programmable Logic Introduction Random Access Memory Memory Decoding Error Detection and Correction Read Only Memory Programmable Logic Array Programmable Array Logic Sequential Programmable Devices

23 Contents (If time permits) 8 Design at the Register Tr a n s f e r L e v e l Introduction Register Transfer Level Notation Register Transfer Level in HDL Algorithmic State Machines (ASMs) Design Example (ASMD Chart) HDL Description of Design Example Sequential Binary Multiplier Control Logic HDL Description of Binary Multiplier Design with Multiplexers Race Free Design (Software Race Conditions) Latch Free Design (Why Waste Silicon?) Other Language Features