AQA 7517 4.6.5.1: Using Boolean algebra
The free BugBot lessons that teach this point, a robot to try it on, and the past-paper questions that test it.
What it covers
Ordinary algebra has rules you use without thinking: a + b = b + a, and a × (b + c) = ab + ac. Boolean algebra has rules too, some the same as ordinary algebra and some surprisingly different. With them you can rewrite an expression into a simpler one that is guaranteed to have the same truth table, which means a circuit with fewer gates, or a program condition that is easier to read.
- The identities
- The laws
- Two ways to prove an equation
- Laws in robot code
Or do it in the simulator, with tasks that mark themselves
Lessons that teach it
- A8.3 Boolean identities and laws Boolean algebra and logic circuits
The identities, commutation, association, distribution, double negation and absorption, proved by truth table. - A8.4 De Morgan's laws Boolean algebra and logic circuits
Breaking the bar and changing the sign, NAND and NOR, and rewriting the robot's loop condition. - A8.5 Simplifying expressions Boolean algebra and logic circuits
A method for simplifying by algebra, worked exam-style examples, and checking the result. - A8.6 Karnaugh maps Boolean algebra and logic circuits
Gray code order, grouping rules for two to four variables, wrap-around groups, and reading off the expression. - A8.9 Project: the robot's safety logic Boolean algebra and logic circuits
From a rule table to a Karnaugh map, a simplified expression, a proof and a robot that stops for the right reasons.
Try it on a robot
The task from A8.3 Boolean identities and laws, running here. Change the program and press Run.
The specification is AQA's own document; this page says which of our lessons teach point 4.6.5.1 and is not endorsed by the board.