tailieunhanh - Lecture Digital logic design - Lecture 7: Minimization with karnaugh maps

The main contents of the chapter consist of the following: K-maps: an alternate approach to representing Boolean functions; K-map representation can be used to minimize boolean functions; easy conversion from truth table to K-map to minimized SOP representation; simple rules (steps) used to perform minimization; leads to minimized SOP representation. | Lecture 7 Minimization with Karnaugh Maps 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 Overview K-maps: an alternate approach to representing Boolean functions K-map representation can be used to minimize Boolean functions Easy conversion from truth table to K-map to minimized SOP representation. Simple rules (steps) used to perform minimization Leads to minimized SOP representation. Much faster and more more efficient than previous minimization techniques with Boolean algebra. credential: bring a computer die photo wafer : This can be an hidden slide. I just want to use this to do my own planning. I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20. Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs. x y F 0 0 1 0 1 1 1 0 0 1 1 0 Karnaugh maps Alternate way of representing Boolean function All rows of truth table represented with a square Each square represents a minterm Easy to convert between truth table, K-map, and SOP Unoptimized form: number of 1’s in K-map equals number of minterms (products) in SOP Optimized form: reduced number of minterms 0 1 y x 0 1 1 0 0 1 0 1 y x 0 1 x’y’ xy’ xy x’y x y F = Σ(m0,m1) = x’y + x’y’ Boolean Cubes and Boolean Functions Boolean Cubes and Boolean Functions A Boolean n-cube uniquely represents a Boolean function of n variables if | Lecture 7 Minimization with Karnaugh Maps 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 Overview K-maps: an alternate approach to representing Boolean functions K-map representation can be used to minimize Boolean functions Easy conversion from truth table to K-map to minimized SOP representation. Simple rules (steps) used to perform minimization Leads to minimized SOP representation. Much faster and more more efficient than previous minimization techniques with Boolean algebra. credential: bring a computer die photo wafer : This can be an hidden slide. I just want to use this