slide02 digital logic operations and functions

517212: Digital Logic Design บทที่ 2 - หนาที่และการทำงานของวงจรดิจิทัล

12 พฤศจิกายน 2555

ตัวปฏิบัติการพื้นฐานทางลอจิกระบบดิจิทัลนั้นสรางจากพื้นฐานทางตรรกศาสตร

จอรจ บูล (George Boole) นักคณิตศาสตรชาวอังกฤษไดสรางพีชคณิตเชิงตรรก (Boolean Algebra) ขึ้นมาในชวงทศวรรษที่ 19 ซึ่งภายหลังไดนำมาประยุกตใชในการออกแบบและสรางระบบดิจิทัล

ตัวปฏิบัติการเชิงตรรกที่ใชเปนพื้นฐานและควรทราบนั้นมีอยูเพียง 3 แบบไดแก

NOT

AND

OR

NOT Negation

Output is the opposite of the input, that’s all.

The symbol:

Note: There is only one input and one output for this op!

AND

The output will be HIGH only when all the inputs are HIGH.

The symbol:

Note: there may be more than two inputs.

OR

The output will be HIGH when one or more inputs are HIGH.

The symbol:

Basic Logic FunctionsRoadmap to what we are going to learn:

–Comparison function

–Arithmetic functions

–Code conversion function

–Encoding function

–Decoding function

–Data selection function

–Storage function

–Counting function

ComparisonA basic comparator compares two quantities and

indicates whether or not they are equal.

–Think about conditional statement like if or things like that in programming.

ArithmeticAdder is the key-element circuit of

binary arithmetic.

–You can add (of course, it’s the adder).

–You can subtract using adder with special treatment on input number.

–You can multiply using adder with the help of other circuits.

–You can also divide with series of circuits in conjunction of adder.

Code Conversion

A code converter changes one form of coded information into another coded form, i.e.:

–binary-to-BCD

–binary-to-Gray code

–etc.

Encoding and Decoding Encoder converts information, such as a decimal number

or an alphabetic character, into some coded form.

Decoder does the opposite.

Data Selection Multiplexer (MUX)

–Switches digital data from several input lines on a single output line in a special time sequence.

Demultiplexer (DEMUX)

–Does the opposite.

Storage This function is

required in most digital systems.

It can memorize a bit of a group of bits and retain the information as long as necessary.

–Flip-flops

–Registers

–etc

CountingCounting is one of the most important

function in digital systems.

–Think about the loop in programming, you cannot accomplish unless you have some sort of counter.

To count, the counter must remember the present numbers it can go to the next proper number in sequence.

Integrated Circuits (ICs)

Fixed-Function ICs

http://www.bbc.co.uk/schools/gcsebitesize/design/images/dt_chip.jpg

http://www.tiscali.co.uk/reference/encyclopaedia/hutchinson/images/c01356.jpg

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Complexity Classifications for Fixed-Function ICs Small-scale integration (SSI)

– Up to 10 gate circuits

Medium-scale integration (MSI)

– 10-100 gate circuits

Large-scale integration (LSI)

– 100-10,000 gates

Very large-scale integration (VLSI)

– 10,000-100,000 gates

Ultra large-scale integration (ULSI)

– More than 100,000 gates

Programmable Logic

PL devices can be programmed to perform specified logic functions using software.

–Hardware Description Language (HDL)

A design can be implemented faster and with less cost (small volume).

Just remember the name:

–Field Programmable Gate Array (FPGA)

–Complex Programmable Logic Device (CPLD)

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