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Physics 3330
Experiment #9
Spring2012
Digital Electronics I: Logic, Flip-Flops, and Clocks
Purpose
This experiment introduces some of the fundamental circuit elements of digital electronics. These include
three kinds of logic gate, two kinds of flip-flop (single bit memory), and the 555 timer chip used as a digital
clock
Introduction
In almost all experiments, the signals that represent physical quantities start out as analog waveforms. To
display and analyze the information contained in these signals, they must be converted to digital data. Often
this is done inside a commercial instrument such as an oscilloscope or a lock-in amplifier, which is
connected to a computer through a digital interface. In other cases data acquisition cards are added to a
computer chassis and the analog signals can be connected directly to the computer. Scientists usually buy
their data acquisition equipment rather than build it, so they often don‟t have to know too much about the
digital circuitry that makes it work. Almost all data is analyzed with a computer, but like other users
scientists don‟t often have to know much about the digital circuitry inside their computers. We emphasize
analog electronics in the course because scientists usually have to know much more about it to design and
build their experiments.
On the other hand, there are plenty of reasons to know something about digital methods. The author of our
text (physicist Paul Horowitz) has built custom digital signal processors to search for signs of
extraterrestrial intelligence in radio telescope signals, and particle physicists have built customized
computer hardware to make calculations in quantum chromodynamics (the theory of the strong force). If
you try to repair a commercial instrument like a modern lock-in you will find that it is full of digital
electronics. The trend in modern instrument design is to do as much digitally as possible; even the front-
panel knobs are not really analog controls, rather they are coded switches or optical encoders that generate
digital data directly. An increasing number of analog parts can be controlled digitally, for example you can
buy digital potentiometers that behave exactly like an analog pot, but look more like an op-amp chip, and
instead of controlling the position of the wiper with a knob, you send a digital code into some of the extra
pins.
In digital circuits the voltage on a wire takes one of only two values called logic HIGH and logic LOW,
corresponding to a binary 1 or 0. Information is conveyed by the pattern of HIGH and LOW voltages. A
single wire can convey just one bit of information at any one time. When the information to be conveyed
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requires more than a single bit, either more wires can be used to convey data (parallel digital data), or a
sequence of bits can be sent over time as HIGH‟s and LOW‟s moving along a single wire (serial digital
data).
Analog information can be translated into digital form by a device called an Analog-to-Digital Converter
(ADC). A set of N bits has 2N possible different values. If you try to represent an analog voltage by 7 bits,
your uncertainty will be about 1%, since there are 27 = 128 possible combinations of 7 bits. For higher
accuracy you will need more bits. There is also a device called a Digital-to-Analog Converter (DAC) that
can convert digital data back into an analog waveform. You can choose either serial or parallel ADCs and
DACs, depending on whether you are using serial or parallel digital data.
In this experiment, we will learn about the most basic elements of digital electronics, from which more
complex circuits, including computers, can be constructed. Logic gates perform logical operations like
AND and OR. The gates we will use are made of bipolar transistors and they come from a family of
devices called TTL (transistor-transistor logic). There are many other logic families (some made of
MOSFETs) offering various trade-offs between speed, power consumption, supply voltage, and output
drive capability (see H&H 9.01, and for the most recent families see the Logic Selection Guide at Texas
Instruments, www.ti.com). Logic gates alone can be used to construct arbitrary combinatorial logic (they
can generate any truth-table), but to create a machine that steps through a sequence of states like a
computer does, we need also memory and a clock.
The fundamental single-bit memory element of digital electronics is called a flip-flop. We will study two
types, called SR (or RS) and JK. The flip-flops we have chosen are also from the TTL family. A digital
clock is a repeating digital waveform used to step a digital circuit through a sequence of states. We will
introduce the 555 timer chip and use it to generate a clock signal. Digital circuits able to step through a
sequence of states with the aid of flip-flops and a clock are called sequential logic.
Readings
1. FC Chapter 11 (digital electronics)
2. H&H Chapter 8. Everything is this chapter is good to know about, but sections 8.01, 8.02, 8.04, 8.07-
8.10, 8.12, 8.16 are most relevant. Also have a look at section 5.14 on the 555 timer chip.
3. (Optional) Diefenderfer 11.1-11.5, 12.1-12.5; Brophy Ch. 9 and pages 272-290; The TTL Cookbook, by
Don Lancaster, SAMS (1974).
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Theory
LOGIC STATES
The voltage in a digital circuit is allowed to be in only one of two states: HIGH or LOW. We usually
abbreviate these as HI and LO.
HI is taken to mean logical (1) or logical TRUE. LO is taken to mean logical (0) or logical FALSE.
In the TTL logic family (see Figure 9.1), any voltage in the range 2.8 to 5.0 V is HI, and any voltage in the
range 0 to 0.8 V is LO.
Any voltage outside this range is undefined, and therefore illegal, except briefly during transitions. If a TTL
circuit is given a voltage in this undefined range, it might, unpredictably, interpret it as either a “1” or a
“0.” We will sometimes refer to HI as the “5 volt” level, and LO as the “0 volt” level.
LOGIC GATES
The flow of digital signals is controlled by transistors in various configurations depending on the logic
family (see H&H 8.09 for details). For most purposes we can imagine that the logic gates are composed of
ideal switches with just two states: OPEN and CLOSED. The state of a switch is controlled by a digital
signal. The switch remains closed so long as a logical (1) signal is applied. A logical (0) control signal
keeps it open.
Logic signals interact by means of gates. The three fundamental gates AND, OR, and NOT, are named after
the three fundamental operations of logic that they carry out. The AND and OR gates each have two inputs
and one output. The output state is determined by the states of the two inputs.
The function of each gate is defined by a truth table, which specifies the output state for each possible
combination of input states. The output values of the truth tables can be understood in terms of two
switches. If the switches are in series, you get the AND function. Parallel switches perform the OR
operation. The most common gates are shown in Fig. 9.2. A bubble after a gate or at an input indicates
NOT.
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The three compound gates NAND, NOR and XOR can be made from AND, OR, and NOT. NAND means
an AND gate followed by a NOT, while NOR means an OR gate followed by a NOT. The EXCLUSIVE-
OR (XOR) is similar to OR but it has a LO output if both inputs are HI, so you can think of it as one OR
the other but NOT both.
NAND and NOR are more common than AND and OR because with the help of DeMorgan‟s theorems
they can be used to simplify complex circuits (see below).
When several gates are combined to perform a complex logical operation, a good design uses as few as
possible. Boolean Algebra, the mathematics of two valued variables, is the theoretical tool used to simplify
complex logical expressions.
BOOLEAN ALGEBRA
Fundamental laws
We imagine a logical variable,
A,
that takes on the values 0 or 1. If
A = 0
then
Ā
= 1
and if
A = 1
then
Ā
= 0
. Here are some obvious identities using the AND, OR and NOT operations. Looking at these
identities you can see why the ‘plus’ symbol was chosen for OR and ‘time’ was chosen for AND.
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Equality
Two Boolean expressions are equal if and only if their truth tables are identical.
Associative Laws
(A+B)+C = A+(B+C)
(AB)C=A(BC)
Distribution Laws
A(B+C) = AB+AB
(A+AB) = A)
(A+
Ā
B) = A+B
(A+B)
(A+C) = (A+BC)
DeMorgan’s Theorems
Example of Proof
Each of the above equalities is a theorem that can be proved. Let’s do an example by directly comparing
the truth tables for the left and right sides. We take on DeMorgan’s first theorem for two variables,
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