1. Chapter 1 Introduction to Digital Systems Design ECEn 224

2. 2 Digital vs. Analog Analog systems represent information using physical quantitiesAnalog systems represent information using physical quantities –Voltage on a wire, magnetic field strength Digital systems represent information using binary digits, or bitsDigital systems represent information using binary digits, or bits –1 or 0, high or low, on or off

3. 3 Positional Number Systems Two discrete values are insufficient for most applicationsTwo discrete values are insufficient for most applications We combine bits to represent more valuesWe combine bits to represent more values We use a positional number system for binary just like we do in decimalWe use a positional number system for binary just like we do in decimal

4. 4 Positional Number Systems Decimal, base 10, means we have 10 digits (0-9)Decimal, base 10, means we have 10 digits (0-9) Decimal example:Decimal example: 1032 10 = 1 x10 3 + 0 x10 2 + 3 x10 1 + 2 x10 0 Hexadecimal, base 16, means we have 16 digits (0-9, A-F)Hexadecimal, base 16, means we have 16 digits (0-9, A-F) Hexadecimal example:Hexadecimal example: 2A5 16 = 2 x16 2 + 10 x16 1 + 5 x16 0 = 512 + 160 + 5 = 677 Binary, base 2, follows the same patternBinary, base 2, follows the same pattern Binary example:Binary example: 1011 2 = 1 x2 3 + 0 x2 2 + 1 x2 1 + 1 x2 0 = 8 + 0 + 2 + 1 = 11 Counting in any base is analogous to counting in decimalCounting in any base is analogous to counting in decimal

5. 5 Digital vs. Analog Analog thermometerAnalog thermometer –0V to 10V, could be used to represent 0° to 100° F –Each 1/10 th volt represents 1 degree Digital thermometerDigital thermometer –7-bit binary number could be used to represent 0° to 127° F –Seven bits can be used to represent the numbers 0 to 127

6. 6 Digital Precision How would you represent 10.5° F?How would you represent 10.5° F? Analog example: 1.05VAnalog example: 1.05V Digital example: ????Digital example: ???? –0001010 2 = 10 10 –0001011 2 = 11 10 –We must either add bits or decrease the range

7. 7 Digital Precision 9-bit thermometer, 0° to 127.75° F9-bit thermometer, 0° to 127.75° F –Each discrete number increase represents 0.25° F –10.5° F  10.5/0.25 = 42 = 101010 2 7-bit thermometer, 0° to 12.7° F7-bit thermometer, 0° to 12.7° F –Each discrete number represents 12.7°/127 = 0.1° F –10.5° F  10.5/0.1 = 105 = 1101001 2 It is not possible to represent all values exactly using digital representationIt is not possible to represent all values exactly using digital representation –Example: 1/3 can’t be represented in binary, just like it can’t be represented in decimal

8. 8 Example: Analog Photography An analog camera uses a chemical reaction in the film when exposed to lightAn analog camera uses a chemical reaction in the film when exposed to light The amount of exposure is directly related to the amount of light that hits the filmThe amount of exposure is directly related to the amount of light that hits the film

9. 9 Example: Digital Photography A digital camera uses an array of light- sensitive receptors that measure the light as a binary numberA digital camera uses an array of light- sensitive receptors that measure the light as a binary number Image quality is determined mostly by two factors:Image quality is determined mostly by two factors: –The number of bits per pixel –The number of pixels per image

10. 10 Example: Digital Photography 1284x897 pixels, 24-bit color 1284x897 pixels, 6-bit color 100x70 pixels, 24-bit color 100x70 pixels, 6-bit color

11. 11 Analog vs. Digital Storage Analog storage mediums fade over time due to gradual physical degradationAnalog storage mediums fade over time due to gradual physical degradation –Photos turn yellow with time –Cassette audio tapes lose their clarity Digital storage mediums don’t “fade” like analogDigital storage mediums don’t “fade” like analog –If a 0 or 1 fades it will still be a 0 or 1 –A.jpg image taken 10 years ago is exactly the same today

12. 12 Analog vs. Digital Storage Making an analog copy implies measuring the storage mediumMaking an analog copy implies measuring the storage medium –Always introduces some errors –Copies of copies are even worse Making digital copies implies distinguishing 0’s from 1’s so copies are exactMaking digital copies implies distinguishing 0’s from 1’s so copies are exact –Copies can be made without any error –Copies of copies are identical

13. 13 Analog vs. Digital Processing Modern computers and digital circuits make it easy to do extremely complex processingModern computers and digital circuits make it easy to do extremely complex processing Digital processing allows precision and error to be exactly predictedDigital processing allows precision and error to be exactly predicted

14. 14 Combinational vs. Sequential Circuits Digital circuits consist of binary inputs and outputsDigital circuits consist of binary inputs and outputs In combinational circuits, the output is a direct function of its inputsIn combinational circuits, the output is a direct function of its inputs In sequential circuits the output depends on the current input and previous inputsIn sequential circuits the output depends on the current input and previous inputs –Sequential circuits contain memory that tracks state –A clock is used to signal when to change states A B C D X Y

15. 15 Combinational vs. Sequential Combinational example: Clock chimeCombinational example: Clock chime –Inputs: seconds and minutes –Output: chime –Behavior: Output chime is 1 if and only if seconds is 0 and minutes is 0, 15, 30, or 45. Sequential example: CounterSequential example: Counter –Inputs: inc and clk –Output: count –Behavior: Increment count on clk edge if and only if inc is 1