The following will be discussed in this chapter: Number system/inter-conversion, complements; boolean algebra; more logic functions: NAND, NOR, XOR; minimization with karnaugh maps; more karnaugh maps and don’t cares; NAND and XOR implementations; circuit analysis and design procedures; binary adders and subtractors; magnitude comparators and multiplexers; encoders, decoders and demultiplexers. | DLD Lecture 18 Recap Give qualifications of instructors: DAP teaching computer architecture at Berkeley since 1977 Co-athor of textbook used in class Best known for being one of pioneers of RISC currently author of article on future of microprocessors in SciAm Sept 1995 RY took 152 as student, TAed 152,instructor in 152 undergrad and grad work at Berkeley joined NextGen to design fact 80x86 microprocessors one of architects of UltraSPARC fastest SPARC mper shipping this Fall Recap Number System/Inter-conversion, Complements Boolean Algebra More Logic Functions: NAND, NOR, XOR Minimization with Karnaugh Maps More Karnaugh Maps and Don’t Cares NAND and XOR Implementations Circuit Analysis and Design Procedures Binary Adders and Subtractors Magnitude Comparators and Multiplexers Encoders, Decoders and DeMultiplexers Digital Signals Decimal values are difficult to represent in electrical systems. It is easier to use two voltage values than ten. Digital Signals have two basic states: 1 (logic “high”, or H, or “on”) 0 (logic “low”, or L, or “off”) Digital values are in a binary format. Binary means 2 states. A good example of binary is a light (only on or off) on off Power switches have labels “1” for on and “0” for off. Number Systems Decimal is the number system that we use Binary is a number system that computers use Octal is a number system that represents groups of binary numbers (binary shorthand). It is used in digital displays, and in modern times in conjunction with file permissions under Unix systems. Hexadecimal (Hex) is a number system that represents groups of binary numbers (binary shorthand). Hex is primarily used in computing as the most common form of expressing a human-readable string representation of a byte (group of 8 bits). Number Systems System Base Symbols Used by humans? Used in computers? Decimal 10 0, 1, 9 Yes No Binary 2 0, 1 No Yes Octal 8 0, 1, 7 No No Hexa- decimal 16 0, 1, 9, A, B, F No No Conversion Among Bases The possibilities: | DLD Lecture 18 Recap Give qualifications of instructors: DAP teaching computer architecture at Berkeley since 1977 Co-athor of textbook used in class Best known for being one of pioneers of RISC currently author of article on future of microprocessors in SciAm Sept 1995 RY took 152 as student, TAed 152,instructor in 152 undergrad and grad work at Berkeley joined NextGen to design fact 80x86 microprocessors one of architects of UltraSPARC fastest SPARC mper shipping this Fall Recap Number System/Inter-conversion, Complements Boolean Algebra More Logic Functions: NAND, NOR, XOR Minimization with Karnaugh Maps More Karnaugh Maps and Don’t Cares NAND and XOR Implementations Circuit Analysis and Design Procedures Binary Adders and Subtractors Magnitude Comparators and Multiplexers Encoders, Decoders and DeMultiplexers Digital Signals Decimal values are difficult to represent in electrical systems. It is easier to use two voltage values than ten. Digital Signals have two basic states: 1 .
