BUILDING COMPUTER CIRCUITS prepared by Burak Galip ASLAN September, 2006 BOOLEAN LOGIC AND GATES CONTROL CIRCUITS

Boolean logic 1815 – 1864 English mathematician and logician Based on symbolic logic TRUEFALSE Binary 1Binary 0 An expression that results in a value of either TRUE or FALSE Boolean expression 2 < 5a > 7

Some Boolean operators pqp + q TTT TFT FTT FFF pqp. q TTT TFF FTF FFF p~ p TF FT ORANDNOT inputsoutput binary operators unary operator

Gates An electronic device that operates on a collection of binary inputs to produce a binary output gate

AND gate (from two transistors)

OR gate (from two transistors)

NOT gate (one transtistor)

Building computer circuits A collection of gates that transforms a set of binary inputs into a set of binary outputs, and the values of the outputs depend only on the current values of the inputs combinational circuit

Building computer circuits sequential circuit

A circuit construction algorithm construct truth table construct sub-expression with AND & NOT gates construct sub-expression with OR gates construct circuit diagram sum-of-products algorithm For each output column

Control circuits multiplexer

Control circuits decoder

Control circuits multiplexerdecoder

Summary What is Boolean logic? Relation between Boolean logic and gates Combinational circuits (an introduction)

An Invitation to Computer Science, 1st Edition (1995) (Schneider & Gersting) ( Section 4.2 ) Wikipedia & Google September, 2006 References