Transcript Lectures/Lect 4 - Combinational Logic

Combinational Logic
Circuits – Gates
9/15/09 - L4 Combinational Logic Gates
Copyright 2009 - Joanne DeGroat, ECE, OSU
1
Class 4 outline
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Binary Logic and Gates
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Basic Gates
Implemented Gates
Material from section 2-1 of text
9/15/09 - L4
Combinational Logic Gates
Copyright 2009 - Joanne DeGroat, ECE, OSU
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Basic Gates
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Gates are the base level elements of digital
systems.
Gates are used to implement Boolean Logic
functions.
Will start with one level circuits or just a
single gate.
Then move on to two or more levels of logic
circuits.
9/15/09 - L4
Combinational Logic Gates
Copyright 2009 - Joanne DeGroat, ECE, OSU
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Logic gates implementation
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Logic gates, having two distinct and stable
states, high and low, are implemented today
using interconnected MOS transistors (most
common).
Today CMOS – Complementary Metal Oxide
Semiconductor – technology is most common.
Have had a steady progression of technology
used for the implementation of digital circuits.
9/15/09 - L4
Combinational Logic Gates
Copyright 2009 - Joanne DeGroat, ECE, OSU
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Past technologies
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RTL – Resistor Transistor Logic –
implemented with resistors and bipolar
transistors
TTL – Transistor Transistor Logic –
implemented with bipolar transistors
NMOS – n-type MOS transistors –
implemented with one transistor configured as
a MOS resistor – similar in philosophy to
RTL
9/15/09 - L4
Combinational Logic Gates
Copyright 2009 - Joanne DeGroat, ECE, OSU
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Basic Functions
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AND
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Represented by a dot (·) or the absence of an operator.
May be written
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Z = X AND Y
z = x AND y
Z=X·Y
Z = XY
Meaning: Result is TRUE if, and only if, both X and Y
are TRUE
Verbal– John and Mary went to the dance and to be true,
they both went to the dance.
9/15/09 - L4
Combinational Logic Gates
Copyright 2009 - Joanne DeGroat, ECE, OSU
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Basic Functions
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OR
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Represented by the + operator symbol
Examples
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Z = X OR Y
Z = x OR Y
Z=X+Y
Meaning: Result is TRUE if at least one of X and Y,
or both, are TRUE.
Verbal – John or Mary went to the dance. Meaning
either John went to the dance, Many went to the
dance, or both of them went to it.
9/15/09 - L4
Combinational Logic Gates
Copyright 2009 - Joanne DeGroat, ECE, OSU
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Basic Functions
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NOT
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Represented by a bar ¯ over the symbol or the
word NOT
Examples
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Z = NOT X
Meaning: True if X is False
9/15/09 - L4
Combinational Logic Gates
Copyright 2009 - Joanne DeGroat, ECE, OSU
False if X is True
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Truth table and gate symbols
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AND function
9/15/09 - L4
Combinational Logic Gates
OR function
Copyright 2009 - Joanne DeGroat, ECE, OSU
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Truth table and gate symbols
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NOT
9/15/09 - L4
Combinational Logic Gates
Copyright 2009 - Joanne DeGroat, ECE, OSU
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But gates are electronic elements
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And have
voltages over
time that are
interpreted as
logic values over
time
9/15/09 - L4
Combinational Logic Gates
Copyright 2009 - Joanne DeGroat, ECE, OSU
11
Basic gates with more than 2 inputs
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It is often the case that we have 3 input AND
gates or 3 inputs OR gates.
Sometimes, even have 4 input gates.
Some logic equations have many terms
ANDed together. In MOS these many input
gates are not readily feasible. Therefore, use
multiple levels of logic.
9/15/09 - L4
Combinational Logic Gates
Copyright 2009 - Joanne DeGroat, ECE, OSU
12
Class 4 assignment
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Covered section 2.1
Problems for hand in
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Problems for practice
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None today
2-1
do it – This is an important one
Section 2.2
9/15/09 - L4
Combinational Logic Gates
Copyright 2009 - Joanne DeGroat, ECE, OSU
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