Before you can read the parent note, you must own every piece of notation it throws at you. We build each one from zero: plain words → the picture → why the topic needs it.
Picture a set of switches on the left and one lamp on the right, wired through gates. Flip switches → lamp settles to on or off. There is no "remember what it was before." (Contrast this with a memory circuit — see Synchronous vs Asynchronous Circuits.)
The topic needs this because a hazard is a combinational phenomenon: it lives in the wires between input and output, in the moment before settling.
Recall Why is "no memory" important for hazards?
Because the wrong value is only transient ::: it disappears once inputs settle; if the circuit had memory it could lock in the glitch, which is a different (worse) problem.
Picture a wire as a pipe that is either empty (0) or full (1).
Why the topic needs it: a glitch is described entirely as a sequence of these values in time, like 1→0→1. You cannot describe a hazard without first agreeing that a wire holds exactly one of two values.
We use three operations. Each is a physical gate (a small circuit) and a symbol in algebra.
Why the topic needs all three: the classic hazard is built precisely from an input feeding an AND directly and also feeding another AND through a NOT. The NOT is the villain — it adds a delay the direct path does not have.
Recall Evaluate
F=AB+BˉC at A=1,B=0,C=1.
F=(1)(0)+(0)(1)=0+(1)(1)=0+1=1 ::: so F=1.
Now stack the symbols. F=AB+BˉC reads: "F is 1 if (A AND B) is true, OR if (NOT-B AND C) is true."
Picture: each product term is one path of AND-gates that can raise the output to 1; the final OR gate collects all the paths.
See Sum of Products and Product of Sums Forms for how any function can be written either way.
Why the topic needs this: static-1 hazards are analysed in SOP (handing off between product terms that make a 1); static-0 hazards are analysed in POS (handing off between sum terms that make a 0). Same idea, mirror image.
Everything above is timeless algebra. Real gates need time.
Picture: send a pulse into a gate; the output copy comes out a little later, shifted right on a time axis. See Propagation Delay and Gate Timing.
Picture two runners starting together, taking routes of different length, meeting again at the finish. For a moment the fast runner has arrived and the slow one hasn't — they disagree.
Why the topic needs it: a hazard is exactly the moment of disagreement between reconvergent paths. No unequal delay ⇒ no hazard. This is the heart of the whole topic.
Recall What is the minimum ingredient list for a static hazard?
One input that changes, reaching the output by two reconvergent paths of different delay ::: (classically, direct vs. through an inverter).
Picture a heartbeat trace: flat at "high", drops to "low", back to "high". The notation 1→0→1 is just the sequence of heights the output line takes — a dip.
Why the topic needs it: the entire classification (static-1, static-0, dynamic) is defined by counting transitions in time, so you must be fluent reading these height-sequences.
Picture a small grid of boxes; stepping one box left/right/up flips a single input from 0 to 1 or back. See Karnaugh Maps and Prime Implicants.
Why the topic needs it: a static-1 hazard shows up visually as two adjacent 1-cells sitting in two different circles — moving between them is a "handoff" from one product term to another, and during the handoff both can drop to 0.
Picture: a third circle drawn over the gap between the two original circles, so there is no bare handoff. See Consensus Theorem and Redundancy. Adding it is the cure: the bridging term holds the output at 1 throughout the change.
Recall What is the consensus of
AB and BˉC?
AC ::: the variable B (true in AB, complemented in BˉC) is dropped, leaving the shared partners A and C.
The left branch (levels → gates → functions) gives you what the circuit computes. The middle branch (delay → reconvergent paths → timing) gives you why glitches appear in time. The right branch (K-map → consensus) gives you the cure. All three meet at the parent topic.
