L T P C 3 1 0 UNIT I BOOLEAN ALGEBRA AND LOGIC GATES 4 9 Review of Binary Number Systems – Binary Arithmetic – Binary Codes – Boolean Algebra and Theorems – Boolean Functions – Simplifications of Boolean Functions Using Karnaugh Map and Tabulation Methods – Implementation of Boolean Functions using Logic Gates. UNIT II COMBINATIONAL LOGIC 9 Combinational Circuits – Analysis and Design Procedures - Circuits for Arithmetic Operations – Code Conversion – Hardware Description Language (HDL). UNIT III DESIGN WITH MSI DEVICES 9 Decoders and Encoders – Multiplexers and Demultiplexers – Memory and Programmable Logic – HDL for Combinational Circuits UNIT IV SYNCHRONOUS SEQUENTIAL LOGIC 9 Sequential Circuits – Flip flops – Analysis and Design Procedures - State Reduction and State Assignment – Shift Registers – Counters – HDL for Sequential Circuits. UNIT V ASYNCHRONOUS SEQUENTIAL LOGIC 9 Analysis and Design of Asynchronous Sequential Circuits - Reduction of State and Flow Tables – Race-Free State Assignment – Hazards – ASM Chart. L: 45 T: 15 Total: 60 TEXT BOOK 1. M. Morris Mano, ―Digital Design‖, 3rd Edition, Pearson Education, 2007. REFERENCES 1. 2. Charles H. Roth, ―Fundamentals of Logic Design‖, 5th Edition, Thomson Learning, 2003. Donald D. Givone, ―Digital Principles and Design‖, Tata McGraw-Hill, 2007.
UNIT I BOOLEAN ALGEBRA AND LOGIC GATES
SYLLABUS : Review of Binary Number Systems Binary Arithmetic Binary Codes Boolean Algebra and Theorems Boolean Functions Simplifications of Boolean Functions Using Karnaugh Map and Tabulation Methods Implementation of Boolean Functions using Logic Gates.
UNIT 1 BOOLEAN ALGEBRA AND MINIMIZATION 1.1 Introduction: The English mathematician George Boole (1815-1864) sought to give symbolic form to Aristotle‘s system of logic. Boole wrote a treatise on the subject in 1854, titled An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities, which codified several rules of relationship between mathematical quantities limited to one of two possible values: true or false, 1 or 0. His mathematical system became known as Boolean algebra. All arithmetic operations performed with Boolean quantities have but one of two possible Outcomes: either 1 or 0. There is no such thing as ‖2‖ or ‖-1‖ or ‖1/2‖ in the Boolean world. It is a world in which all other possibilities are invalid by fiat. As one might guess, this is not the kind of math you want to use when balancing a checkbook or calculating current through a resistor. However, Claude Shannon of MIT fame recognized how Boolean algebra could be applied to on-and-off circuits, where all signals are characterized as either ‖high‖ (1) or ‖low‖ (0). His1938 thesis, titled A Symbolic Analysis of Relay and Switching Circuits, put Boole‘s theoretical work to use in a way Boole never could have imagined, giving us a powerful mathematical tool for designing and analyzing digital circuits. Like ‖normal‖ algebra, Boolean algebra uses alphabetical letters to denote variables. Unlike ‖normal‖ algebra, though, Boolean variables are always CAPITAL letters, never lowercase. Because they are allowed to possess only one of two possible values, either 1 or 0, each and every variable has a complement: the opposite of its value. For example, if variable ‖A‖ has a value of 0, then the complement of A has a value of 1. Boolean notation uses a bar above the variable character to denote complementation, like this: