Digital Logic ECE 2500
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This 7 page Class Notes was uploaded by Lizeth Hegmann on Wednesday September 30, 2015. The Class Notes belongs to ECE 2500 at Western Michigan University taught by Dean Johnson in Fall. Since its upload, it has received 79 views. For similar materials see /class/216772/ece-2500-western-michigan-university in Engineering Electrical & Compu at Western Michigan University.
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Date Created: 09/30/15
ECE 2500 Spring 2009 LECTURE SUBJECT TITLES Reading Assignment logic circuits and design logic circuits Computer structure INTRODUCTION amp NUMBER SYSTEMS Major Application of Digital Logic the design of microprocessor chips in computers or handhelds iPod Architecture From electronicshowstuffworkscomipod3htm Microprocessor chip Memory SDRAM 256 MB Peripherals a Click Wheel capacitive sensing controller electronicshowstuffworkscomipod4htm b Hard drive 30 GB Display 320 X 240 pixel LCD electronicshowstuffworkscomcd2htm New iPhoneiPod Touch Display electronicshowstuffworkscomipod touch2htm d Video controller chip e Audio controller chip Power supply battery Motherboard circuit board that provides chip mounting and supplies signals via bus to all components N O 0quot Digital Logic Devices 1 Register holds multiple bits of binary data 2 Port a register interfacing to the outside world 3 ALU adds contents of 2 registers 4 Bus A path by which data may flow from one register to another in parallel 5 Encoder Encodes or compresses data 6 Decoder Decodes or expands data Also used to make table selections such as in a memory 7 MUX Selects between many data sources 8 ROM An storage array that can be read word by word chosen by an address 9 RAM A storage array that also can be written 10 USB cable A path by which data packets may be transferred serially to ports from a hub 110ptical Disc Storage CDDVD ROM from which blocks of data can be read 12 Hard Disk Drive A magnetic storage device from which blocks of data can be stored ampread 13 USB drive A ROM device which can transfer data in blocks over a USB cable 14 Microcontroller A processing device consisting of an ALU registers ports and RAM Notes B byte 8 bits b K21 1024103 29512 23256 Mkxk22 1o6 GKXM23 109 rapidrepaircom and ipodmechaniccom are both located in Kalamazoo MI 15 Microprocessor More powerful processor that has extensive memory and multiple ALUs 16 LCD display a display device which uses a 2d decoder array and a controller Number systems table comparison of important number systems including decimal base 10 2 binary base 2 3 octal base 8 and 4 hexadecimal base 16 number systems Music data files for the iPod From computerhowstuffworkscommp31htm 1 Music voltage is sampled at 44100 Hz and each sample is converted to 2 bytes of binary information 2 This decimal to binary or hex conversion is done with an analog to digital AD converter 3 3 minute song consumes 32MB of file space 4 MP3 applies compression to reduce file size from 32 MB to approximately 3 MB General Number Systems Representation 1 Juxtapositional notation for representation of a number N 2 Polynomial representation for N Numberbase Conversion The process of converting N from one numberbase representation to another There are three cases to consider 1 Power series method to convert N to base 10 2 Dividemultiply method to convert base 10 Nto any other base ie music sampling above 3 Base 2k conversions binary to hex or octal Representing Negative Numbers 2 s complement format allows numbers to be added or subtracted only by use of addition 2 s Complement Method le take a 2 s complement of a number N 1 Complement all the bits of N 2 Add 1 to the result This is N39 3 The sign of N or N is shown by the most significant bit 0 1 2 bytes 16 bits 4 hex digits Note NN 0 Binary Codes 1 ASCII 7 bit code for all characters 2 Gray 3 Hamming an error correction code ECC Compute HC for datain Compute HC for dataout 0 Compare differences in H0 bits and add those positions to form bit error position o m iPod hard drive data format From computerhowstuffworkscomharddisk7htm 1 Toshiba 18 platter stores up to 7500 songs 2 Tracks are divided up into a number of fixed length sectors consisting of a Preamble for head synchronizing b Data field 0 E00 field Hamming or ReedSolomon iPhonelPod TouchNano flash drive data format 1 Solid state flash drive identical to USB drive 2 Memory is broken up into are divided up into a number of fixed length blocks similar to the tracks of magnetic disks Blocks consist of a Data field b ECC field BOOLEAN ALGEBRA and Notes COMBNA TIONAL LOGIC CIRCUITS Binary numbers are also used as truth values or logic values Logic defined the process of classifying information Binary logic or more commonly digital logic is the process of classifying information into two distinct classes eg TRUE FALSE truth values Yes No CLOSE OPEN relay positions blown intact fuse state ON OFF switch positions 1 0 binary numbers or Logic 1 Logic 0 Logic design is based upon the three logic operators Binary Logic Operations Variables 1 AND ZZX39nyy Jack and Jill stories 20R zxy 3 NOT z 3 also written as z x39 Binary Logic Operations Numbers OR XOR AND 000 0600 00 011 0 11 01 10 11 ll HOOO 101 1601 111 1 10 Two Level Logic Circuits with ANDOR gates Examples will be given to describe 1 ANDOR circuits sum of product SOP 2 ORAND circuits product of sum P08 3 XORXOR circuits These circuits can also be described algebraically with the use of an algebra system for logic variables called Boolean Algebra Fundamental properties of Boolean Algebra Each xy and z are elements ofB 01 1 Identities P3 P4 Dual x 0 x x 0 0 x 1 1 x 1 x 2 Commutativity P1 xyyx xyyx 3 Associativity P2 xyz xy z xyzxyz 4 Distributivity P8 xCvzxyxz xyzXyxz 5 Existence of tile complement P5 There exists an element called x such that xx I x 3 6 0 6 Involution P7 x 7 Absorption P12 xxyx xxyx 8 Adjacency P9 xyxfzx xyxfx 9 DeMorgan39s Law P1 1 xyzxyz xyzx372 Boolean Functions and Logic Circuits Examples will now be given to show Deriving a Boolean functions from circuits and vice versa l Developing truth tables A Simplifying Boolean functions pattern matching some of the Boolean properties and theorems DeMorgan s Laws Shows Equivalent Graphical Symbols for Logic Gates Examples will be given to describe 1 NAND gate drawn with an OR symbol 2 NOR gate drawn with an AND symbol 3 NOTs built from NANDs and NORs Boolean algebra is an algebraic formulation of thought and reason originally conceived by the mathematician George Boole in 1854 The right hand properties are duals ofthe left hand ones is obtained by interchanging dots with plusses and 1s with 0s The most common theorems to which pattern matching is applied are Absorption Logic Adjacency and DeMorgan s theorem A literal in a Boolean function is a variable or its complement
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