Digital Electronics

Lecture Notes for Digital Electronics

Raymond E. Frey
Physics Department
University of Oregon
Eugene, OR 97403, USA
rayfrey@cosmic.uoregon.edu
March, 2000

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 doescreate 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.
Thedrawback 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 incredible 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 caseof 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

True (T)
False (F)

Voltage State
(positive true)
High (H)
L

1
0

Voltage State
(negative true )
Low (L)
HThe 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

the labelled point is at +5 Volts. With a closed switch, the labelled point is connected to
ground, with a 5 Volt drop across the resistor and a current of I = V /R= 5 mA through
it.)

+5 V

1k

switch open

Figure 1: Illustration for labelling logic states (“positive true”).
With the convention known as “negative true”, the label would be changed to “switch
closed” with a bar over it: switch closed. Our statement becomes:
The labelled voltage is Low (High) when the label’s stated function is True (False).
So in the figure, the stated function(switch closed) is true when the voltage is low. The bar
¯
¯
¯
is meant to envoke the boolean inversion operation: T = F, F = T, T = T, and so forth.

1.2

Binary Arithmetic

Each digit in binary is a 0 or a 1 and is called a bit, which is an abbreviation of binary digit.
There are several common conventions for representation of numbers in binary.
The most familiar is unsigned binary....