Boolean Foundations#

Gates obey algebra.

Every combinational circuit is a Boolean expression in disguise, and every Boolean expression can be drawn as gates. That equivalence is the most useful lever in digital design: a function can be written as a truth table, reduced with algebra or a Karnaugh map, and only then committed to hardware — trading gates for speed, or speed for gates, on purpose rather than by accident. This is also where the difference between the intended logic and the momentary glitches a real circuit produces first shows up.

Sections#

• Truth Tables — The exhaustive specification every combinational function starts from.
• Boolean Algebra — Identities and laws for manipulating logic expressions.
• De Morgan’s Theorems — Why NAND and NOR are interchangeable with everything else.
• Canonical Forms (SOP & POS) — Minterms, maxterms, and the standard ways to write a function.
• Karnaugh Maps — Visual minimization: fewer gates, fewer surprises.
• Hazards & Glitches — The transient outputs a correct truth table doesn’t predict.