Transcript Document

Number Systems, Data Types,
Codes Logic Gates:
An Introduction
University
Cork
IRELAND
College
Number Systems
• Base
• Digit values
• Positional values -- integer powers of
base
• Zero (0) to represent nothing in a
given position
• Value of number = sum of products of
digits and their positional values
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Computer Number Systems
University
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System
Base
Digits
Binary
2
0, 1
Octal
8
Decimal
10
Hexadecimal
16
0, 1, 2, 3, 4, 5,
6, 7
0, 1, 2, 3, 4, 5,
6, 7, 8, 9
0-9, A, B, C,
D, E, F
Octal and Binary Digits
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Octal
Binary
Octal
Binary
0
1
2
3
000
001
010
011
4
5
6
7
100
101
110
111
Hexadecimal and Binary Digits
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Hex
Binary
Hex
Binary
0
1
2
3
4
5
6
7
0000
0001
0010
0011
0100
0101
0110
0111
8
9
A
B
C
D
E
F
1000
1001
1010
1011
1100
1101
1110
1111
Data Types
• Numeric data
– binary integer
– floating-point
– decimal value
• String data
– a.k.a. character data
– one character per byte
– 8-bit code such as ASCII or EBCDIC
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ASCII and EBCDIC Codes.
Character
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ASCII
EBCDIC
0
1
2
3
4
5
6
7
8
9
0101 0000
0101 0001
0101 0010
0101 0011
0101 0100
0101 0101
0101 0110
0101 0111
0101 1000
0101 1001
1111 0000
1111 0001
1111 0010
1111 0011
1111 0100
1111 0101
1111 0110
1111 0111
1111 1000
1111 1001
A
B
C
D
E
F
G
H
I
1010 0001
1010 0010
1010 0011
1010 0100
1010 0101
1010 0110
1010 0111
1010 1000
1010 1001
1100 0001
1100 0010
1100 0011
1100 0100
1100 0101
1100 0110
1100 0111
1100 1000
1100 1001
Character
ASCII
EBCDIC
J
K
L
M
N
O
P
Q
R
1010 1010
1010 1011
1010 1100
1010 1101
1010 1110
1010 1111
1011 0000
1011 0001
1011 0010
1101 0001
1101 0010
1101 0011
1101 0100
1101 0101
1101 0110
1101 0111
1101 1000
1101 1001
S
T
U
V
W
X
Y
Z
1011 0011
1011 0100
1011 0101
1011 0110
1011 0111
1011 1000
1011 1001
1011 1010
1110 0010
1110 0011
1110 0100
1110 0101
1110 0110
1110 0111
1110 1000
1110 1001
Logic Gates
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• Electronic circuits which combine digital
signals according to the Boolean algebra are
referred to as logic gates
• Gates because they control the flow of
information.
• Positive logic is an electronic representation
in which the true state (1) is at a higher
voltage, while negative logic has the true
state (0) at a lower voltage.
Logic Circuit Families
• Logic circuits are grouped into families, each with their
own set of detailed operating rules. Some common logic
families are:
– RTL: resistor-transistor logic,
– DTL: diode-transistor logic,
– TTL: transistor-transistor logic,
• TTL is normally used for small-scale integrated circuit units
– NMOS: N-channel metal-oxide silicon,
• MOS features very low power consumption and is used in VLSI
technology
– CMOS: complementary metal-oxide silicon and
– ECL: emitter-coupled logic.
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• ECL is very fast The. The TTL is normally used for small-scale
integrated circuit units
Logic Gate Building Blocks
• Symbols and truth tables for the four basic twoinput gates: a) AND, b) NAND, c) OR, d) NOR
and e) the inverter.
– The open circle is used to indicate the NOT or negation
function and can be replaced by an inverter in any
circuit.
– A signal is negated if it passes through the circle.
– Any logic operation can be formed from NAND or
NOR gates or a combination of both. We also
commonly have gates with more than two inputs.
– Inverter gates can be formed by applying the same logic
signal to both inputs of an NOR or NAND gate.
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Examples
of Logic
Gates
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