Boolean algebra and logic circuits

All six gates and the exam notations, circuits from problems and truth tables, the laws of Boolean algebra and De Morgan, simplifying by algebra and by Karnaugh map, adders, and D-type flip-flops, with the robot's sensor conditions as the circuits.

Module A8A level9 lessons

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  1. A8.1 Logic gates and notation NOT, AND, OR, XOR, NAND and NOR, the notation each board uses, and why NAND alone can build anything.
  2. A8.2 Circuits, expressions and truth tables Reading and drawing circuits, defining a problem in Boolean logic, and sum of products from a truth table.
  3. A8.3 Boolean identities and laws The identities, commutation, association, distribution, double negation and absorption, proved by truth table.
  4. A8.4 De Morgan's laws Breaking the bar and changing the sign, NAND and NOR, and rewriting the robot's loop condition.
  5. A8.5 Simplifying expressions A method for simplifying by algebra, worked exam-style examples, and checking the result.
  6. A8.6 Karnaugh maps Gray code order, grouping rules for two to four variables, wrap-around groups, and reading off the expression.
  7. A8.7 Half adders and full adders The full adder's expressions, building it from half adders, and chaining full adders into a ripple carry adder.
  8. A8.8 D-type flip-flops and clocks Clock signals, edge triggering, the D-type flip-flop as one bit of memory, registers and a divide-by-two counter.
  9. A8.9 Project: the robot's safety logic From a rule table to a Karnaugh map, a simplified expression, a proof and a robot that stops for the right reasons.