1 / 10

Boolean Logic and Circuits

Boolean Logic and Circuits. ELEC 311 Digital Logic and Circuits Dr. Ron Hayne Images Courtesy of Cengage Learning. Exclusive-OR (XOR). Boolean Algebra. Identity laws: 1. X + 0 = X 1D. X • 1 = X 2. X + 1 = 1 2D. X • 0 = 0 Idempotent laws:

chinara
Download Presentation

Boolean Logic and Circuits

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Boolean Logic and Circuits ELEC 311 Digital Logic and Circuits Dr. Ron Hayne Images Courtesy of Cengage Learning

  2. Exclusive-OR (XOR) 311_03

  3. Boolean Algebra Identity laws: 1. X + 0 = X 1D. X • 1 = X 2. X + 1 = 1 2D. X • 0 = 0 Idempotent laws: 3. X + X = X 3D. X • X = X Involution law: 4. (X')' = X Laws of complements: 5. X + X' = 1 5D. X • X' = 0 311_02

  4. Boolean Algebra Commutative laws: 6. X + Y = Y + X 6D. XY = YX Associative laws: 7. (X + Y) + Z = X + (Y + Z) 7D. (XY)Z = X(YZ) = XYZ Distributive laws: 8. X(Y+Z) = XY + XZ 8D. X + YZ = (X + Y)(X + Z) DeMorgan's laws: 9. (X + Y )' = X'Y' 12D. (XY)' = X' + Y' Simplification theorem: 10. XY+ XY' = X(Adjacency Theorem) 311_02

  5. Minterms and Maxterms 311_04

  6. Sum of Products (SOP) AB'+ CD'E + AC'E' 311_02

  7. Product of Sums (POS) (A + B')(C + D' + E)(A + C'+ E') 311_02

  8. NAND and NOR Gates 311_07

  9. DeMorgan's Laws • (X ∙ Y)' = X' + Y' • (X + Y)' = X' ∙ Y' 311_07

  10. SOP to NAND-NAND G = WXY + YZ 311_07

More Related