DigitalNotes - Lecture Notes for Digital Electronics...

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Lecture Notes for Digital Electronics Raymond E. Frey Physics Department University of Oregon Eugene, OR 97403, USA rayfrey@cosmic.uoregon.edu March, 2000
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1 Basic Digital Concepts By converting continuous analog signals into a finite number of discrete states, a process called digitization , then to the extent that the states are sufficiently well separated so that noise does create errors, the resulting digital signals allow the following (slightly idealized): storage over arbitrary periods of time flawless retrieval and reproduction of the stored information flawless transmission of the information Some information is intrinsically digital, so it is natural to process and manipulate it using purely digital techniques. Examples are numbers and words. The drawback to digitization is that a single analog signal ( e.g. a voltage which is a function of time, like a stereo signal) needs many discrete states, or bits , in order to give a satisfactory reproduction. For example, it requires a minimum of 10 bits to determine a voltage at any given time to an accuracy of 0 . 1%. For transmission, one now requires 10 lines instead of the one original analog line. The explosion in digital techniques and technology has been made possible by the incred- ible increase in the density of digital circuitry, its robust performance, its relatively low cost, and its speed. The requirement of using many bits in reproduction is no longer an issue: The more the better. This circuitry is based upon the transistor, which can be operated as a switch with two states. Hence, the digital information is intrinsically binary . So in practice, the terms digital and binary are used interchangeably. In the following sections we summarize some conventions for defining the binary states and for doing binary arithmetic. 1.1 Binary Logic States The following table attempts to make correspondences between conventions for defining binary logic states. In the case of the TTL logic gates we will be using in the lab, the Low voltage state is roughly 0–1 Volt and the High state is roughly 2 . 5–5 Volts. See page 475 of the text for the exact conventions for TTL as well as other hardware gate technologies. Boolean Logic Boolean Algebra Voltage State Voltage State (positive true) (negative true ) True (T) 1 High (H) Low (L) False (F) 0 L H The convention for naming these states is illustrated in Fig. 1. The “positive true” case is illustrated. The relationship between the logic state and label (in this case “switch open”) at some point in the circuit can be summarized with the following: The labelled voltage is High (Low) when the label’s stated function is True (False) . In the figure, the stated function is certainly true (switch open), and this does correspond to a high voltage at the labelled point. (Recall that with the switch open, Ohm’s Law implies that with zero current, the voltage difference across the “pull up” resistor is zero, so that 1
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the labelled point is at +5 Volts. With a closed switch, the labelled point is connected to
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DigitalNotes - Lecture Notes for Digital Electronics...

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