chap2(4_in_1) - ELEC151 Digital Circuits and Systems...

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ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 2-1 Lecture Note #2 Boolean Algebra Basic definitions and axioms 2-1, 2-2 Laws and theorems of Boolean algebra 2-3, 2-4 – Design process and Boolean algebra Two-level canonical forms 2-5 – Incompletely specified functions More logic functions 2-6, 2-7 – NOT, AND, OR, NAND, NOR, XOR, XNOR, and more – Positive and negative logic Integrated circuits 2-8 – CMOS, TTL, … – OrCAD (in laboratory) Reading Assignments: – Chapter 2 ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 2-2 Boolean Algebra/Logic Circuits Boolean Algebra – In 1854, a mathematician, George Boole , developed an algebraic system to handle only two variables, TRUE and FALSE Digital Circuits – In 1938, Claude Shannon (father of information theory) showed (in his Master’s thesis!) how to map Boolean Algebra to digital circuits: Structure of Boolean Algebra – A set of elements B – Two binary operators, AND (•) and OR (+) – One unary operator, NOT (’) Primitive Gates – AND, OR and NOT ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 2-3