Transcript Logic Elements - ODU Computer Science

COMPUTER ARCHITECTURE &
OPERATIONS I
Instructor: Yaohang Li
Review
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Last Class
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Basic of Logic Design
This Class
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Integrated Circuits
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Decoder
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Multiplexor
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PLA
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ROM
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Don’t Care
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Bus
Next Class
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Design of ALU
Integrated Circuit
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Integrated Circuit (IC)
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A small electronic device made out of a semiconductor
material
Classifications
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SSI (small-scale integration)
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MSI (medium-scale integration)
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3,000~100,000 electronic components per chip
VLSI (very large-scale integration)
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100~3,000 electronic components per chip
LSI (large-scale integration)
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up to 100 electronic components per chip
100,0000 to 1,000,0000 electronic components per chip
ULSI (ultra large-scale integration)
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More than 1 million electronic components per chip
Decoder
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Decoder
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A logic block that has n-bit input and 2n
outputs, where only one output is asserted for
each input combination
If the input is i (in binary),
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then output i is 1
others are 0
Decoder Example
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3-8 Decoder
Multiplexor
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Multiplexor
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A selector
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The output is selected by an input control
Implementation of a Multiplexor
n-input Multiplexor
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A Multiplexor can have n-inputs
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Require
selective inputs
Implementation of an n-input Multiplexor
Two-level Logic
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Try to Remember: Any Boolean Logic
function can be implemented with only
NOT, AND, OR functions
We can also find that all logic functions
can be written in a canonical form
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Sum of Product
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Logical Sum (OR) of terms joined by Product
(AND)
Product of Sum
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Logical Product (AND) of terms joined by Sum
(OR)
Example
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Consider a logic function
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Equivalent to sum of products
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Equivalent to product of sums
In Class Exercise
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Considering the following truth table for D,
write the function of D using sum of
products
Answer
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Combinations that D is 1
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Answer
Programmable Logic Array
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Programmable Logic Array (PLA)
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Two stages of logic
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An array of AND gates (product terms)
An array of OR gates
PLA Example
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Considering the following table, implement
the PLA for D, E, F
Another PLA Representation
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Dot in the AND plane
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Input, or its inverse,
occurs in the product
term
Dot in the OR plane
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Corresponding product
term appears in the
corresponding output
Read Only Memory
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Read Only Memory (ROM)
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Programmable ROM (PROM)
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Can be burnt using a device called a “ROM programmer”
Erasable Programmable Read Only Memory
(EPROM)
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Has a set of locations that can be read
Contents of these locations are fixed
Data in the ROM can be deleted under ultra-violet rays
EEPROM (Electrically Erasable Read Only
Memory)
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Data in the ROM can be erased by a simple electric
current
ROM
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Height
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Width
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m inputs
2m addressable entries (input lines)
n outputs (functions)
2n output bits
mxn is the shape of the ROM
ROMs and PLAs
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PLA is partially decoded
ROM is fully decoded
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Contains a full output word for every possible input combination
Always contain more entries than PLA
PLA (7 entries)
ROM (8 entries – 1 unused)
Don’t Care
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Don’t Care
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Output Don’t Care
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We don’t care about the value of an output for
some input combination
Input Don’t Care
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We don’t care about the actual values
An output only depends on some of the inputs
Advantages of Don’t Care
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Easier to optimize the implementation of a
logic function
Example of Don’t Cares
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Original Truth Table
Example of Don’t Cares
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Output Don’t Cares
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Input Don’t Cares
Array of Logic Elements
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Bus
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In logic design, a collection of data lines that is treated
together as a single logical signal
Shared collection of lines with multiple sources
32-bit wide 2-to-1 multiplexor
Summary
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Integrated Circuits
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Decoder
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Multiplexor
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PLA
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ROM
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Don’t Care
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Bus
What I want you to do
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Review Chapter 1
Review Appendix B