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Logic Design

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,

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Logic Design

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  1. 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, …

  2. 1 2 3 4 2 value value time time What Does “Digital” Mean? • Digital signal • Finite possible values • Ex: button pressed on a keypad • Analog signal • Inifinite possible values • Ex: voltage on a wire created by microphone digital signal analog signal Possible values: 1.00, 1.01, 2.0000009, ... infinite possibilities Possible values: 0, 1, 2, 3, or 4. That’s it. 4 3 2 1 0

  3. 3 3 Volts 2 2 original signal received signal 1 1 0 0 time How fix -- higher, lower, ? 01 10 11 10 11 a2d Volts digitized signal 1 1 0 0 time time Can fix -- easily distinguish 0s and 1s, restore 01 10 11 10 11 same Digitized signal not perfect re-creation, but higher sampling rate and more bits per encoding brings closer. d2a 3 Volts 2 1 0 time Example of Digitization Benefit • Analog signal (e.g., audio) may lose quality • Voltage levels not saved/copied/transmitted perfectly • 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 lengthy transmission (e.g, cell phone) time lengthy transmission (e.g, cell phone) Let bit encoding be: 1 V: “01” 2 V: “10” 3 V: “11”

  4. Digitized Audio: Compression Benefit • Digitized audio can be compressed • e.g., MP3s • A CD can hold about 20 songs uncompressed, but about 200 compressed • Compression also done on digitized pictures (jpeg), movies (mpeg), and more • Digitization has many other benefits too • Example compression scheme: • 00 --> 0000000000 • 01 --> 1111111111 • 1X --> X 0000000000 0000000000 0000001111 1111111111 00 00 10000001111 01

  5. Benefits of Digital • Reliable storage (CD, DVD, …) • Compression (MP3, JPEG, …) • Reliable transmission (cell phones, digital TVs, …) Conversion from Analog to Digital Technology

  6. Digital Encodings and Binary Numbers We can represent any digital data using only binary digits (0 and 1), or bits. ASCII encoding: A 01000001 B 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)

  7. A: Remaining quantity Binary Number 0 0 0 0 0 0 23 32 16 8 4 2 1 23 0 1 0 0 0 0 -16 32 16 8 4 2 1 7 7 0 1 0 1 0 0 -4 32 16 8 4 2 1 8 is more than 7, can’t use 3 3 0 1 0 1 1 0 -2 32 16 8 4 2 1 1 1 0 1 0 1 1 1 -1 32 16 8 4 2 1 0 Done! 23 in decimal is 10111 in binary. Converting from Decimal to Binary Numbers:Subtraction Method Example • Q: Convert the number “23” from decimal to binary

  8. 8 A F 4 3 2 1 0 16 16 16 16 16 8 A F 1000 1010 1111 h e x bina r y h e x bina r y 0 0000 8 1000 1 0001 9 1001 2 0010 A 1010 3 0011 B 1011 4 0100 C 1100 5 0101 D 1101 6 0110 E 1110 7 0111 F 1111 F 0 Base Sixteen: Another Base Sometimes Used by Digital Designers • 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

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