LearnTronics
From Boolean Expressions to Gate Circuits
Turn algebra into gates — one operation at a time
A Boolean expression is also a construction plan. Parentheses and intermediate operations tell us how to build the logic.
Example
Break it into small pieces:
Now the schematic almost draws itself: AND A and B, invert C, then OR those two results.
The same expression can become relay logic
For relay contacts, A•B may be represented by two normally open contacts in series. The OR operation may be represented by parallel branches. ~C may be represented by a normally closed C contact.
This is one reason Boolean algebra is such a good bridge between abstract logic and physical control circuits.
But timing can change the physical behavior
Two circuits can implement the same steady-state Boolean expression and still behave differently for a very short time while signals are changing. Different paths may have different propagation delays.
Those temporary effects are called logic hazards or glitches. They become important in faster and more complex circuits, so algebraic equivalence is only one part of real design.