LearnTronics
Equivalent Gates and De Morgan's Laws
Different drawings can mean the same logic
The bubble convention leads directly to two very useful identities called De Morgan's laws.
Read the first one in words
“It is NOT true that A AND B are both true” means the same thing as “A is NOT true OR B is NOT true.”
That is why a NAND gate can also be drawn as an OR-shaped gate with bubbles on both inputs.
Read the second one in words
“It is NOT true that A OR B is true” means both A and B must be false.
That is why a NOR gate can also be drawn as an AND-shaped gate with bubbles on both inputs.
“Bubble pushing”
Designers sometimes speak informally of pushing bubbles through a gate. When an inversion moves from the output side to all of the input sides, the gate changes:
The Boolean function remains equivalent when De Morgan's law is followed correctly.
A truth table is one way to verify De Morgan's laws. In the Boolean-algebra lessons that follow, we will also derive them from ordinary-language reasoning and from the algebraic laws themselves — without depending on a truth table.
Check one with a truth table
| A | B | ~(A • B) | ~A + ~B |
|---|---|---|---|
| 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
The last two columns match row for row, so the two expressions are logically equivalent.
Try these yourself
Why this matters later
Once active-LOW signals, bubbles, NAND/NOR logic, and De Morgan's laws become familiar, real digital schematics become much easier to read. A designer can choose whichever equivalent form makes the circuit clearer or better matches the available ICs.