That's Maths: How barcodes and QR codes work

Virtually everything that you buy in your local supermarket has a curious little zebra-like pattern the size of a postage stamp printed on it. Barcodes, originally devised about 40 years ago to label railroad cars, are now universal on consumer products. But how do they work, and how can we be confident that they are scanned accurately and that we are charged the correct amount for our trolley of groceries?