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Digital Logic Operations and Functions

Digital Logic Operations and Functions. Basic Logic Operations. Logic, as you know it, involves in a making of digital system. George Boole developed ‘Boolean Algebra’ (details later)  it’s applied in the design and analysis of digital systems.

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Digital Logic Operations and Functions

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  1. Digital Logic Operations and Functions

  2. Basic Logic Operations • Logic, as you know it, involves in a making of digital system. • George Boole developed ‘Boolean Algebra’ (details later) it’s applied in the design and analysis of digital systems. • Three basic logic ops you MUST know (to build much more complex circuits) • NOT • AND • OR

  3. 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!

  4. AND • The output will be HIGH only when all the inputs are HIGH. • The symbol: • Note: there may be more than two inputs.

  5. OR • The output will be HIGH when one or more inputs are HIGH. • The symbol:

  6. Basic Logic Functions • Roadmap 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

  7. Comparison • A 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.

  8. Arithmetic • Adder 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.

  9. 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.

  10. Encoding and Decoding • Encoder converts information, such as a decimal number or an alphabetic character, into some coded form. • Decoder does the opposite.

  11. 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.

  12. 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

  13. Counting • Counting 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.

  14. Integrated Circuits (ICs)

  15. Fixed-Function ICs http://www.bbc.co.uk/schools/gcsebitesize/design/images/dt_chip.jpg http://www.dolphin.fr/corporate/announcements/pressrelease/2002/images/dsair.jpg http://www.tiscali.co.uk/reference/encyclopaedia/hutchinson/images/c01356.jpg

  16. 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

  17. 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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