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Chapter 7
Logic Circuits
1. State the advantages of digital technology
compared to analog technology.
2. Understand the terminology of digital
circuits.
3. Convert numbers between decimal, binary,
and
other forms.
5. Understand the binary arithmetic
operations
used in computers and other digital
systems.
6. Interconnect logic gates of various types
to
implement a given logic function.
7. Use Karnaugh maps to minimize the
number
of gates needed to implement a logic
function.
Advantages of the Digital
Approach
Provided that the noise amplitude is not too
large, the logic values represented by a digital
signal can still be determined after noise is
added.
With modern IC technology, it is possible to
manufacture exceedingly complex digital
circuits economically containing 10s of
millions of transistors.
Definitions
Positive versus Negative Logic
Digital Words
In parallel transmission, an n-bit word is
transferred on n wires, one wire for each bit,
plus a common or ground wire. In serial
transmission, the successive bits of the word
are transferred one after the other with a
single pair of wires.
Binary Numbers
743.210  7  10 2  4  101  3  100  2  10 1
1
1101.12  7  2  1  2  0  2  1  2  1  2  13.510
3
2
1
0
Gray Code
Complement Arithmetic
The one’s complement of a binary number is
obtained by replacing 1s by 0s, and vice
versa.
01001101
10110010 (one’s complement)
The two’s complement of a binary number
is obtained by adding 1 to the one’s
complement, neglecting the carry (if any) out
of the most significant bit.
Complements are useful for representing
negative numbers and performing subtraction
in computers.
Subtraction Using Two’sComplement Arithmetic
Overflow and Underflow
In performing arithmetic using two’scomplement arithmetic, we must be aware of
the possibility of overflow in which the result
exceeds the maximum value that can be
represented by the word length in use.
AA  A
A1  A
A0  0
AB  BA
ABC    ABC  ABC
AA 0
A A
A  B  C  A  B  C   A  B  C
AB  C   AB  AC
A 0  A
A1 1
A A 1
A A  A
Boolean algebra expressions can be
implemented by interconnection of AND
gates, OR gates, and inverters.
De Morgan’s Laws
ABC  A  B  C
D  E  F   D E F
If the variables in a logic expression are
replaced by their inverses, the AND
operation is replaced by OR, the OR
operation is replaced by AND, and the entire
expression is inverted, the resulting logic
expression yields the same values as before
the changes.
Chapter 12
Field-Effect Transistors
1. Understand MOSFET operation and small
signal model (compare to BJTs).
2. See how FETs are used to build gates in
CMOS Integrated Circuits (ICs) for
computers.
NMOS AND PMOS
TRANSISTORS
MOSFET Summary
The Fixed- Plus Self-Bias
Circuit
The Small-Signal Equivalent
Circuit
In small-signal midband analysis of FET
amplifiers, the coupling capacitors, bypass
capacitors, and dc voltage sources are
replaced by short circuits. The FET is
replaced with its small-signal equivalent
circuit. Then, we write circuit equations and
derive useful expressions for gains, input
impedance, and output impedance (like
earlier BJTs).
CMOS Inverter
CMOS NAND Gate
CMOS NOR Gate
NAND, NOR, and XOR Gates
Sum-of-Products
Implementation
Product terms that include all of the input
variables (or their inverses) are called
minterms.
In a sum-of-products expression, we form a
product of all the input variables (or their
inverses) for each row of the truth table for
which the result is logic 1. The output is the sum
of these products.
Product-of-Sums
Implementation
Sum terms that include all of the input
variables (or their inverses) are called
maxterms.
In a product-of-sums expression, we form a
sum of all the input variables (or their inverses)
for each row of the truth table for which the
result is logic 0. The output is the product of
these sums.
Many useful combinatorial circuits known as decoders,
encoders, or translators are available as integrated
circuits.
Karnaugh Maps
DIGITAL SIGNAL
PROCESSING
Conversion of Signals from
Analog to Digital Form
If a signal contains no components with
frequencies higher than fH, the signal can be
exactly reconstructed from its samples,
provided
that the sampling rate fs is selected to be
more than twice fH.
Digital Lowpass Filter
yn  ayn  1  1  a xn
 T
a
1 T
Chapter 8
Microcomputers
1. Identify and describe the functional blocks
of a
microcomputer.
2. Select the type of memory needed for a
given
application.
An embedded computer is part of a product,
such as an automobile, printer, or bread
machine, that is not called a computer.
A microcomputer or microcontroller is a
complete
computer containing the CPU, memory, and
I/O on a single silicon chip.
This computer, in which the instructions and
data are
stored in the same memory, has von Neumann
architecture (also known as Princeton
architecture).
MEMORY TYPES
(1) Read-and-write memory (RAM)
(2) Read-only memory (ROM)
(3) Mass storage - Disk, Flash
(non volatile)
Selection of Memory
1. The trade-off between speed and cost
2. Whether the information is to be stored
permanently or must be changed frequently
3. Whether data are to be accessed in random
order or in sequence
ASSEMBLY-LANGUAGE
PROGRAMMING
In general, assembly language statements
take the form:
LABEL
COMMENT
INSTRUCTION/DIRECTIVE
OPERAND
Directives are used to give commands to the
assembler.
1. Compilers translate a higher level language, such as
C and convert it into assembly (machine language)
for a particular computer. Typically one C statement
will generate several (5-10) assembly language
statements
2. Most work is currently done using compilers and C.
It’s faster and more cost effective to develop new
applications.
3. Some tools like Labview can automatically generate
C code.