PHYSICS & ELECTRONICS / BOOLEAN ALGEBRA / PAGE 41 OF 50
De Morgan's Theorems
Swapping AND and OR through inversion.
De Morgan's theorems show how to push a bar through an expression. The inverse of an AND equals the OR of the inverses, and the inverse of an OR equals the AND of the inverses. In each case break the bar and change the operator.
Original diagram: de morgan's theorems
This means a NAND gate is the same as an OR gate with inverted inputs, and a NOR gate is the same as an AND gate with inverted inputs. NAND and NOR are universal gates, since any logic function can be built from either one alone.
- Break the bar, change the sign.
- Useful for converting between gate types.
- Check with a truth table to be sure.
KEY IDEA
(A·B)' = A' + B' and (A+B)' = A' · B'Browse all 50 physics and electronics pages | Back to the course index