ECE 2500 Spring 2012 LECTURE SUBJECT TITLES Subject Sequence Marcovitz Textbook Reading Assignment The Digital World Howstuffworks.com Number System Conventions 1.1-1.3 Boolean algebra 2.2-2.4, 2-7-2.8 Logic Gates and CIrcuits 2.6 minterms and K-maps 2.5, 3.1 Maxterms and Kmaps 3.2-3.4 Important types of CLCs 4.2-4.5 ROM, PLD & RAM Structures 4.6 Sequential Logic Circuits 5.1-5.2 Flip-flops and Clocks 5.3 Sequential logic circuit analysis and design 6.1-6.4 Important Types of SLCs 7.1-7.3THE DIGITAL WORLD Notes: Major Application of Digital Logic: the design of microprocessor chips in computers & mobile devices. iPod Architecture From: electronics.howstuffworks.com/ipod3.htm 1. Microprocessor chip 2. Memory (SDRAM 256 MB) 3. Peripherals a. Click Wheel (capacitive sensing controller) electronics.howstuffworks.com/ipod4.htm b. Hard drive (30 GB) c. Display (320 x 240 pixel LCD) electronics.howstuffworks.com/lcd2.htm 4. iPod Touch differences a. Smaller electronics b. Touch display (480 x 320 pixel x 2) electronics.howstuffworks.com/ipod-touch2.htm Digital Data Types 1. Numeric a. Integer i. Unsigned (count values) ii. Signed (add or subtract) b. Floating Point i. Radix (decimal) points ii. Sign, fraction & exponent c. BCD (binary-coded decimal) 2. Nonnumeric a. Characters i. ASCII: 1 B for each of 28 = 256 English and control characters (Latin-1) From: howstuffworks.com/bytes2.htm ii. UNICODE: 2 B for each of 216 = 64K International characters. b. Audio i. Analog waveforms From: howstuffworks.com/analog-digital2.htm ii. A/D Conversion to 16 bits (CD) From: howstuffworks.com/analog-digital3.htm iii. Compression. From: computer.howstuffworks.com/mp32.htm B = byte = 8 bits (b) K = 210 = 1024 ≈ 103 29 = 512 28 = 256 … etc. M = K x K = 220 ≈ 106 G = K x M = 230 ≈ 109 A motherboard is where all the circuit components are mounted. Major components are connected by bus ribbons. One large square chip is numbered PP5020E. Google this number and see if you can identify this chip. Open a text file and type: “ECE 2500”. When you save the file, find the size of the file in bytes. It should be 8 B. It is estimated that there are about 200,000 international characters. UNICODE can handle only ¼ of them. Codecs such as MP3 or AAC (iPod) use pycho acoustics and perceptual coding to compress the file to 10% of its original size.Color codes From: howstuffworks.com/lcd5.htm iv. Red 1 B => 256 shades v. Green 1 B => 256 shades vi. Blue 1 B => 256 shades Digital Logic Components (Process digital data) 1. Register (holds various forms of digital data) 2. Port (a register interfacing data to/from 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 memory location selections) 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) 11. Optical Disc Storage (CD/DVD 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 &read) 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) 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 SYSTEM CONVENTIONS Number systems table: comparison of important number systems, including: 1. decimal (base 10) 2. binary (base 2) 3. octal (base 8), and 4. hexadecimal (base 16) number systems Octal and hexadecimal are encodings of groups of binary #s. The total number of possible shades of colors with a 24 bit color format is: 2563 = 224 = 16 M colorsGeneral Number Systems Representation 1. Juxtapositional notation for representation of a number = N. 2. Polynomial representation for N. Number-base Conversion: The process of converting N from one number-base representation, to another. There are three cases to consider: 1. Power series method to convert N to base 10. 2. Divide/multiply method to convert base 10 N to any other base. (i.e. music sampling, above) 3. Base 2k conversions: binary to hex (or octal). Binary Addition of Integers: 1. Bit by bit addition right to left, with carry bits 2. Subtraction is done by adding numbers encoded in 2’s complement format. 2’s Complement Format: (i.e. “how to take a 2’s complement” of a number N) 1. Complement all the bits of N 2. Add 1 to the result. This is N’. 3. The sign of N (or N’) is shown by the most significant bit: 0 = “+”; 1 = “-“. Error Correction Codes (ECC) 1. Provides self-correction of errors that occur in the data when transporting data. 2. Hamming code a. Compute HC for data-in b. Compute HC for data-out c. Compare differences in HC bits and add those positions to form bit error position 3. Other ECC: Reed-Solomon code ECC in an iPod hard drive From: computer.howstuffworks.com/hard-disk7.htm 1. Toshiba 1.8” platter stores up to 7,500 songs 2. Tracks are divided up into a number of fixed length sectors, consisting of a. Preamble (for head synchronizing) b. Data field c. ECC field (Hamming or Reed-Solomon) 3. Solid-state Drive: Memory is broken up into are divided up into a number of fixed length blocks, similar to the tracks of magnetic disks. Blocks consist only of the Data field and ECC field Note: N + N’ = 0 A preamble field is not necessary in a solid state drive because there is no mechanical motion to sync to. Error correction is one of the most important advantages that digital systems provide over analog systems.BOOLEAN ALGEBRA Notes: 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, e.g. (TRUE, FALSE) = truth values (Yes, No) (CLOSE, OPEN) = relay positions blown, intact = fuse state (ON, OFF) = switch positions (1, 0) = binary numbers, or