Logic gates.

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Presentation transcript:

Logic gates

Computer Design using Digital Circuits Primary circuit component is the “transistor” Billions (literally) can be fabricated on a single integrated circuit (IC) Circuits operate at low voltages (approx. one volt) Transistors are used as simple switches Transistors are connected together into circuits and turn each other on or off depending on how they’re connected Circuit inputs and outputs are in either of two states, high (power supply) voltage, or low voltage (0V) High state is a “one/true”, low state is a “zero/false"– Binary!!!

Electronic Design of a Digital Computer General approach: Wire together electronic components (transistors, in particular) to create gate level “building blocks” Inverter, nand, nor, and more… Use these “gates” to construct higher level modules that implement the basic functions of the computer

Boolean Algebra Based on symbolic logic Designed by George Boole Defines a set of operations on variables that have two states, true or false (or 1 and 0) In symbolic logic, Boolean expressions are manipulated (similar to mathematical statements) In circuit design, basic operations are represented with “logic gate” symbols

Basic Logical Operations (and gate symbols) NOT AND OR

NOT Inverts, or reverses, a Boolean value A’ !A 𝐀 ¬A A OUT F T Truth Table Symbolic representations: A’ !A 𝐀 ¬A

AND A B OUT F T Common representations: Truth Table AB A*B A˄B

OR A B OUT F T Common representations: Truth Table A+B A˅B

Additional Logical Operations NOR NAND An “AND” followed by a “NOT” An “OR” followed by a “NOT” Note: The “bubble” means inversion (NOT) These are easy to implement and commonly used in circuit design

NAND 𝐀𝐁 𝐀∗𝐁 𝐀˄𝐁 !(AB) ¬(A*B) A B OUT F T Truth Table “nand” is the “not”, or inversion, of “and”

NOR 𝐀+𝐁 𝐀˅𝐁 !(A+B) ¬(A ˅ B) A B OUT F T Truth Table “nor” is the “not”, or inversion, of “or”

(Mulit-input NANDs and NORs are easily implemented in a CMOS circuit) More than 2 inputs? 3 input “AND” AND = true if all inputs are true OR = true if any inputs are true A B C OUT F T (Mulit-input NANDs and NORs are easily implemented in a CMOS circuit)

Logisim Circuit Software Build digital circuits Download: http://sourceforge.net/projects/circuit/ Installed in classroom 100% Free We will only use an extremely small subset of functionality available. Basic logic gates Inputs Others See Logisim PowerPoints for more info