Download Presentation
## BOOLEAN ALGEBRA

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**BOOLEAN ALGEBRA**Boolean Algebra**BOOLEAN ALGEBRA**-REVIEW Boolean Algebra was proposed by George Boole in 1853. Basically AND,OR NOT can be expressed as Venn Diagrams Boolean Algebra**Min Terms and Max Terms**Min Terms are those which occupy minimum area on Venn Diagram Max Terms are those which occupy maximum area on Venn diagram. Boolean Algebra**LOGIC GATES**Nand and Norgates are calledUniversal gates as any Boolean function can be realized with the help of Nand and Nor gates only Boolean Algebra**For example, NOT, OR, AND gates can be realized**by only Nand gates. Boolean Algebra**SIMPLIFICATION OF BOOLEAN FUNCTIONS**• Algebraic Method • Tabular Method • K-Map Method • Schienman Method Boolean Algebra**ALGEBRAIC METHOD**• Simplify using algebraic theorems • Advantage: • First Method based on Boolean Algebra theorems • Disadvantage: • No Suitable algorithm to apply (Trial type of method) Boolean Algebra**TABULAR METHOD**• Also called Quine McClusky Method • Advantage: • It may work for any no. of variables • Disadvantage: • Simplification from table is quite involved Boolean Algebra**K-MAP METHOD**• Karnaugh Map. Also called Vietch • Karnaugh Method. • Advantage: • Simplest and Widely accepted • Disadvantage: • Applicable for only upto Six variables Boolean Algebra**SCHIENMAN METHOD**• Columnwise writing of minterms as • decimal numbers and their simplification • Advantage: • Very suitable for computerization. Applicable for any • number of variables. Parallel Processing • Disadvantage: • May not result in most simplified answer for some • problems Boolean Algebra**Steps for simplification:**• Try to find single one’s • 2 one’s • 4 one’s • 8 one’s Always see is a higher combination exists. If a higher combination exists, wait. Be sure that you have managed the lower combination first. Boolean Algebra