Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Logic Design Logic design deals with the basic concepts and tools used to design digital hardware consisting of logic circuits Digital devices: airbags, auto-focus cameras, aircraft navigators, cell phones, credit card readers, digital cameras, DVD players, personal computers, portable music players, … 1 What Does “Digital” Mean? • Analog signal • Digital signal – Inifinite possible values • Ex: voltage on a wire created by microphone – Finite possible values • Ex: button pressed on a keypad 1 2 3 4 2 digital signal Possible values: 1.00, 1.01, 2.0000009, ... infinite possibilities time value value analog signal 4 3 2 1 0 Possible values: 0, 1, 2, 3, or 4. That’s it. time 2 1 0 Digitized version enables near-perfect save/cpy/trn. – “Sample” voltage at particular rate, save sample using bit encoding – Voltage levels still not kept perfectly – But we can distinguish 0s from 1s Let bit encoding be: 1 V: “01” Digitized signal not 2 V: “10” perfect re-creation, but higher sampling 3 V: “11” rate and more bits per encoding brings closer. original signal time a2d 1 digitized signal 0 time 01 10 11 10 11 3 2 1 0 received signal time How fix -- higher, lower, ? 01 10 11 10 11 Volts • 2 lengthy transmission (e.g, cell phone) – Voltage levels not saved/copied/transmitted perfectly 3 lengthy transmission (e.g, cell phone) Analog signal (e.g., audio) may lose quality Volts • Volts Example of Digitization Benefit 1 0 time Can fix -- easily distinguish 0s and 1s, restore d2a 3 2 1 0 time 3 Digitized Audio: Compression Benefit • Digitized audio can be compressed – e.g., MP3s – A CD can hold about 20 songs uncompressed, but about 200 compressed Example compression scheme: 00 --> 0000000000 01 --> 1111111111 1X --> X 0000000000 0000000000 0000001111 1111111111 00 00 10000001111 01 • Compression also done on digitized pictures (jpeg), movies (mpeg), and more • Digitization has many other benefits too 4 Benefits of Digital • Reliable storage (CD, DVD, …) • Compression (MP3, JPEG, …) • Reliable transmission (cell phones, digital TVs, …) Conversion from Analog to Digital Technology 5 Digital Encodings and Binary Numbers We can represent any digital data using only binary digits (0 and 1), or bits. ASCII encoding: A B … 01000001 01000010 … Why binary numbers? Base ten: decimal numbers (0,1,2,3,4,5,6,7,8,9) Base two: binary numbers (0,1) Base eight: octal numbers (0,1,2,3,4,5,6,7) Base sixteen: hexadecimal numbers (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F) 6 Converting from Decimal to Binary Numbers: Subtraction Method Example • Q: Convert the number “23” from decimal to binary A: Remaining quantity Binary Number 23 0 0 32 16 0 8 0 4 0 2 0 1 23 -16 7 0 1 32 16 0 8 0 4 0 2 0 1 7 -4 3 0 1 32 16 0 8 1 4 0 2 0 1 3 -2 1 0 1 32 16 0 8 1 4 1 2 0 1 1 -1 0 0 1 32 16 0 8 1 4 1 2 1 1 8 is more than 7, can’t use Done! 23 in decimal is 10111 in binary. 7 Base Sixteen: Another Base Sometimes Used by Digital Designers 164 163 8 A F 162 161 160 8 A F 1000 1010 1111 hex binary hex binary 0 1 2 3 4 5 6 7 0000 0001 0010 0011 0100 0101 0110 0111 8 9 A B C D E F 1000 1001 1010 1011 1100 1101 1110 1111 • Nice because each position represents four base two positions – Used as compact means to write binary numbers • Known as hexadecimal, or just hex Q: Write 11110000 in hex F0 8