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Csc 2313 (lecture 4)
1. INTRODUCTION TO COMPUTER
SYSTEM
CSC 2313
LECTURE 4
Department of Maths and Computer-Science
Faculty of Natural andApplied Science
BY
UMAR DANJUMA MAIWADA
3. INTRODUCTION
Binary logic consists of binary variables and logical
operations.The variables are designated by letters of
the alphabet such asA, B, C, x, y, z, etc., with each
variable having two and only two distinct possible
values: 1 and O.There are three basic logical
operations:AND, OR, and NOT
Logic gates are primarily implemented using diodes or
transistors acting as electronic switches, but can also
be constructed using vacuum tubes, electromagnetic
relays (relay logic), fluidic logic, pneumatic logic,
optics, molecules, or even mechanical elements.
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4. DIGITAL LOGIC DESIGN
Digital (electronic) circuits are electronics that handle
digital signals
Digital techniques are useful because it is easier to get an
electronic device to switch into one of a number of known
states than to accurately reproduce a continuous range of
values.
They correspond to the false and true values of the Boolean
domain respectively.
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5. LOGIC GATES
logic gate is an idealized or physical device implementing a
Boolean function; that is, it performs a logical operation on one
or more binary inputs, and produces a single binary output.
With amplification, logic gates can be cascaded in the same way
that Boolean functions can be composed, allowing the
construction of a physical model of all of Boolean logic, and
therefore, all of the algorithms and mathematics that can be
described with Boolean logic.
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6. NOT GATE
Inversion, negation”“NOT” symbol → Z= X' (Also called the complement)
NOT gate is more commonly called an inverter
The circle on the symbol is called a bubble, and is used in logic diagrams to indicate a
logic negation between the external logic state and the internal logic state (1 to 0 or vice
versa). On a circuit diagram it must be accompanied by a statement asserting that the
positive logic convention or negative logic convention is being used (high voltage level = 1 or
low voltage level = 0, respectively).
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7. OR GATE
The rest of the class relies on two-valued BooleanAlgebra, i.e. B = {0, 1}We use
variables X,Y, Z,A, B, … and constants 0 and 1. **Note“0”and“1”are also called
identity elements. Binary operators → “+” called “OR”. • “OR” symbol → Z=X+Y.
2-input gates
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9. XOR
The output of a two input exclusive-OR is true only when the two input
values are different, and false if they are equal, regardless of the value. If there
are more than two inputs, the output of the distinctive-shape symbol is
undefined.The output of the rectangular-shaped symbol is true if the
number of true inputs is exactly one or exactly the number following the
"=" in the qualifying symbol.
2-input gates
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18. DE MORGAN EQUIVALENT SYMBOLS
By use of De Morgan's laws, an AND function is identical to an
OR function with negated inputs and outputs. Likewise, an OR
function is identical to an AND function with negated inputs and
outputs.A NAND gate is equivalent to an OR gate with
negated inputs, and a NOR gate is equivalent to anAND gate
with negated inputs.
This leads to an alternative set of symbols for basic gates that
use the opposite core symbol (AND or OR) but with the inputs
and outputs negated. Use of these alternative symbols can make
logic circuit diagrams much clearer and help to show accidental
connection of an active high output to an active low input or
vice versa.
De Morgan's theorem is most commonly used to implement
logic gates as combinations of only NAND gates, or as
combinations of only NOR gates, for economic reasons.
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19. Boolean Algebra Theorems
Purpose of Theorems
TheTheorems & Huntington’s Postulates are key in our ability to reduce
the number of literal (variables) used in a function and therefore reduce
the number of gates required to implement a given function. Sometimes
they are used to simply rearrange the expression so it is easier to
implement.
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23. 23
Utilizing Demorgan’sTheorem NAND and NOR gates may be represented using the other’s
base signal as shown below (“not” circle indicates complement):
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Transforming from one form to another requires only two steps:
1) Complement every input and output.
2) Swap OR and AND gates.
Example: Design an XOR using only NAND gates.
F (A, B) =A ⊕ B
Solution:
F (A, B) =A’.B + B’.A
Apply conversion rules “Complement every input and output; Swap ORs and ANDs
F (A, B) = ((A’.B)’ . (B’.A)’)’
25. BINARY CODED DECIMAL (BCD)
A common way to represent the digits 0 - 9 is by the ten four-bit
patterns
There are six bit patterns (for example 1010) that are not used, and the
question is what to do with them.
The unused bit patterns might simply be ignored. If a decoder
encounters one, perhaps as a result of an error in transmission or an
error in encoding, it might return nothing, or might signal an output
error.
The unused patterns might be mapped into legal values. For example,
the unused patterns might all be converted to 9, under the theory that
they represent 10, 11, 12, 13, 14, or 15, and the closest digit is 9.
They might be decoded as 2, 3, 4, 5, 6, or 7, by setting the initial bit to
0, under the theory that the first bit might have gotten corrupted.
27. ASCII
TheAmerican Standard Code for Information Interchange
Introduced by theAmerican National Standards Institute
(ANSI) in 1963.
ASCII is a seven-bit code, representing the 33 control
characters and 95 printing characters (including space)
The control characters are used to signal special conditions
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29. 8 BITS
ASCII characters follow a leading 0, and thus may be thought of as
the “bottom half ” of a larger code on 8-bit context.
The 128 characters represented by codes between HEX 80 and HEX
FF (sometimes incorrectly called “highASCII” of “extendedASCII”)
have been defined differently in different contexts.
People now appreciate the need for interoperability of computer
platforms, so more universal standards are coming into favor.
Most people don’t want 32 more control characters (indeed, of the
33 control characters in 7-bitASCII, only about ten are regularly
used in text).
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31. REFERENCES
Digital logic Design by Norman BalabanianUniversity of Florida
Bradley Carlson SymbolTechnologies,Inc.
Tinder,Richard F.(2000).Engineering digital design:Revised Second Edition.
pp.317–319.ISBN 0-12-691295-5.Retrieved 2008-07-04.
Bostock,Geoff (1988).Programmable logic devices:technology and applications.
NewYork:McGraw-Hill.ISBN 978-0-07-006611-3.Retrieved 28 November
2012.
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