Digital Logic Operations and Functions

Basic Logic Operations Logic, as you know it, involves in a making of digital system. 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. 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) Three basic logic ops you MUST know (to build much more complex circuits) –NOT –AND –OR

NOT Negation Negation Output is the opposite of the input, that’s all. Output is the opposite of the input, that’s all. The symbol: 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 output will be HIGH only when all the inputs are HIGH. The symbol: The symbol: –Note: there may be more than two inputs.

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

Basic Logic Functions Roadmap to what we are going to learn: 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

Comparison A basic comparator compares two quantities and indicates whether or not they are equal. 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.

Arithmetic Adder is the key-element circuit of binary 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.

Code Conversion A code converter changes one form of coded information into another coded form, i.e.: 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. Encoder converts information, such as a decimal number or an alphabetic character, into some coded form. Decoder does the opposite. Decoder does the opposite.

Data Selection Multiplexer (MUX) Multiplexer (MUX) –Switches digital data from several input lines on a single output line in a special time sequence. Demultiplexer (DEMUX) Demultiplexer (DEMUX) –Does the opposite.

Storage This function is required in most digital systems. 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. It can memorize a bit of a group of bits and retain the information as long as necessary. –Flip-flops –Registers –etc

Counting Counting is one of the most important function in digital systems. 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. 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 design/images/dt_chip.jpg /hutchinson/images/c01356.jpg pressrelease/2002/images/dsair.jpg

Complexity Classifications for Fixed- Function ICs Small-scale integration (SSI) Small-scale integration (SSI) –Up to 10 gate circuits Medium-scale integration (MSI) Medium-scale integration (MSI) – gate circuits Large-scale integration (LSI) Large-scale integration (LSI) –100-10,000 gates Very large-scale integration (VLSI) Very large-scale integration (VLSI) –10, ,000 gates Ultra large-scale integration (ULSI) Ultra large-scale integration (ULSI) –More than 100,000 gates

Programmable Logic PL devices can be programmed to perform specified logic functions using software. 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). A design can be implemented faster and with less cost (small volume). Just remember the name: Just remember the name: –Field Programmable Gate Array (FPGA) –Complex Programmable Logic Device (CPLD)