AQA 7517 4.5.4.3: Signed binary using two's complement
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
At GCSE you added 8-bit numbers, spotted overflow and met two's complement. A level asks for more: the range of an n-bit number as a formula, binary multiplication, a second way to store negatives (sign and magnitude), subtraction done by adding, and exactly when a signed result has overflowed. The robot's motor commands are signed bytes, so these rules decide whether "reverse at 50" arrives as reverse at 50.
- Unsigned binary
- Sign and magnitude
- Two's complement
- Carry is not overflow
- Hexadecimal and signed values
Or do it in the simulator, with tasks that mark themselves
Lessons that teach it
- A7.2 Binary arithmetic and signed integers Data representation
Unsigned addition and multiplication, sign and magnitude, two's complement, subtraction and overflow. - A15.7 Calculation and theory questions Exam preparation
Number representation, floating point, Boolean logic, state machines and complexity answered quickly and checked.
Try it on a robot
The task from A7.2 Binary arithmetic and signed integers, running here. Change the program and press Run.
The specification is AQA's own document; this page says which of our lessons teach point 4.5.4.3 and is not endorsed by the board.