Table of ContentsCombinational logic Possible logic functions of two variables Cost of different logic functions Minimal set of functions An algebraic structure Boolean algebra Logic functions and Boolean algebra Axioms and theorems of Boolean algebra Axioms and theorems of Boolean algebra (cont’d) Axioms and theorems of Boolean algebra (cont’) Axioms and theorems of Boolean algebra (cont’) Proving theorems (rewriting) Proving theorems (perfect induction) A simple example Apply the theorems to simplify expressions From Boolean expressions to logic gates From Boolean expressions to logic gates (cont’d) From Boolean expressions to logic gates (cont’d) Waveform view of logic functions Choosing different realizations of a function Which realization is best? Which is the best realization? (cont’d) Are all realizations equivalent? Implementing Boolean functions Canonical forms Sum-of-products canonical forms Sum-of-products canonical form (cont’d) Product-of-sums canonical form Product-of-sums canonical form (cont’d) S-o-P, P-o-S, and de Morgan’s theorem Four alternative two-level implementationsof F = AB + C Waveforms for the four alternatives Mapping between canonical forms Incompleteley specified functions Notation for incompletely specified functions Simplification of two-level combinational logic The uniting theorem Boolean cubes Mapping truth tables onto Boolean cubes Three variable example Higher dimensional cubes m-dimensional cubes in a n-dimensional Boolean space Karnaugh maps Karnaugh maps (cont’d) Adjacencies in Karnaugh maps Karnaugh map examples More Karnaugh map examples Karnaugh map: 4-variable example Karnaugh maps: don’t cares Karnaugh maps: don’t cares (cont’d) Design example: two-bit comparator Design example: two-bit comparator (cont’d) Design example: two-bit comparator (cont’d) Design example: 2x2-bit multiplier Design example: 2x2-bit multiplier (cont’d) Design example: BCD increment by 1 Design example: BCD increment by 1 (cont’d) Definition of terms for two-level simplification Examples to illustrate terms Algorithm for two-level simplification Algorithm for two-level simplification (example) Combinational logic summary |
Author: Gaetano Borriello |