Transcript chapter 1
Continuous vs. Discrete Analog: Continuous 1000.00 mV 0.00 mV Analog corresponds to real. 0 1 2 3 Digital: Discrete Digital corresponds to symbolic. Seattle Pacific University EE 1210 - Logic System Design DigitalSystems-1 From Analog to Digital 0 1 2 3 125 375 625 875 0.00 mV 250.00 500.00 750.00 1000.00 mV • Our analog signal had an infinite range of values in between 0.00 mV and 1000.00 mV • The new digital signal has only four values: 0,1,2,3 • ‘0’ corresponds to all values from 0 mV to 250 mV, but is represented by the value 125 mV • Likewise for 1,2, and 3 Seattle Pacific University EE 1210 - Logic System Design DigitalSystems-2 The issue of Noise 125 0.00 mV 625 375 250.00 500.00 875 750.00 Digital Analog Sent 150 624 429 987 223 Received 156.2 613.5 401.3 992.1 223.1 1000.00 mV Sent 125 625 375 875 125 Received 131.2 614.5 347.3 880.5 125.1 Becomes 125 625 375 875 125 Noise Margin - The amount of noise that can be added to a digital signal without changing the result. (Above example: +/- 125mV) Seattle Pacific University EE 1210 - Logic System Design DigitalSystems-3 Finite representation 125 0.00 mV 625 375 250.00 500.00 875 750.00 1000.00 mV Analog signal 1000 750 mV 500 Digital signal 250 0 Seattle Pacific University time EE 1210 - Logic System Design DigitalSystems-4 Tradeoffs • Digital signals are limited (finite) - Analog signals are continuous (infinite) • We can always make the analog-to-digital conversion finer-grained • Analog signals are very susceptible to noise Digital signals can tolerate noise • The finer-grained the analog-to-digital conversion is, the smaller the noise margins • Noise beyond the noise margins does really bad things to digital signals Seattle Pacific University EE 1210 - Logic System Design DigitalSystems-5 Other reasons for using Digital Systems • Computers use digital logic • Computers must be spoken to in their own language - digital systems are the way to go • Digital systems are easier to understand • Functions are defined by easy-to-understand binary logic instead of complex differential equations Seattle Pacific University EE 1210 - Logic System Design DigitalSystems-6 Binary Systems • Binary systems have two values • Zero and One • Binary numbers are easy to represent using physical phenomena • All numbers can be represented in binary as well as in any other base Seattle Pacific University Zero ‘0’ False Off Low V 0V Current EE 1210 - Logic System Design One ‘1’ True On High V 5V No Current DigitalSystems-7 Waveforms Digital data can vary over time, making a digital waveform H L Time Rising Edge Falling Edge 100% 90% A Real Waveform 50% 10% 0% Rise Time Seattle Pacific University Fall Time EE 1210 - Logic System Design DigitalSystems-8 Clocks Regular Periodic waveforms are called Clock Signals Period TH TL Period is measured in seconds Frequency = 1/Period, measured in Hertz Example: TH = 3ns, TL = 2ns. What are period and frequency? Period = TH+TL = 5ns Seattle Pacific University Frequency = 1/5ns = 200MHz EE 1210 - Logic System Design DigitalSystems-9 Using a Clock Consider this waveform, carrying digital data: What data does it carry? 101010? 1 0 0 1 0 1 1 0 Apply a clock to it to understand the waveform. Sample it at each falling edge: 10010110 Warning: The sample clock must be the same frequency as the clock that was used to generate the waveform If the second clock was used, we’d have 1100001100111100 Seattle Pacific University EE 1210 - Logic System Design DigitalSystems-10 Timing Diagrams A binary function, F(A,B,C), shown as a timing diagram A B C F A B C F 1 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 Note: This “timing” diagram doesn’t have a time scale – we’ll get to that later Seattle Pacific University EE 1210 - Logic System Design DigitalSystems-11 Number Systems 123410 = 1 x 103 + 2 x 102 + 3 x 101 + 4 x 100 10102 = 1 x 23 + 0 x 22 + 1 x 21 + 0 x 20 =1x8 + 0x4 + 1x2 + 0x1 = 810 + 210 = 1010 n D Pi B i i0 Seattle Pacific University Decimal Binary General formula for converting an n-digit number from base B to decimal (Pi is the ith digit of the number) EE 1210 - Logic System Design DigitalSystems-12 Binary numbers • Binary: Base 2 • Decimal: Base 10 • Hexadecimal: Base 16 • It takes 4 binary digits (bits) to represent the numbers 015 • Each group of 4 binary digits corresponds to exactly one hex digit Seattle Pacific University Decimal Binary 0 0000 1 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 8 1000 9 1001 10 1010 11 1011 12 1100 13 1101 14 1110 15 1111 EE 1210 - Logic System Design Hexadecimal 0 1 2 3 4 5 6 7 8 9 A B C D E F DigitalSystems-13 Binary-to-Decimal Conversion Each bit in a binary number refers to a power of two: 1010011 26 2 5 24 23 22 21 20 64+0+16+0+0+2+1 = 83 Seattle Pacific University 20 21 22 23 24 25 26 27 28 29 210 211 212 213 214 215 216 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 EE 1210 - Logic System Design 1K 2K 4K 8K 16K 32K 64K DigitalSystems-14 Decimal-to-Binary Conversion Start with decimal number N: 25 Subtract largest power of two N 25 - 24 = 25 - 16 = 9 Subtract largest power of two remainder = 9 9 - 23 = 9 - 8 = 1 Repeated Subtraction or sum-of weights method Subtract largest power of two remainder = 1 22=4 is too large - skip Subtract largest power of two remainder = 1 21=2 is too large - skip Subtract largest power of two remainder = 1 1 - 20 = 1 - 1 = 0 Now, we see 2510 = 24 + 23 + 20 = 1 1 0 0 12 Seattle Pacific University EE 1210 - Logic System Design DigitalSystems-15