One from each part of the course. Choose an answer, say how sure you are, then press Check. Every wrong answer tells you why it is wrong.
Every topic has a short note like this one, ending with what the exam asks and what gains the mark.
Meet Bit. Bit is a seagull who lives on the roof of Morag's chip van, and Bit understands exactly two things in this world: chip and no chip.
Ask Bit about the weather, the football or the meaning of life and you get a blank stare. Hold up a chip and you have Bit's full attention. That is not much of a personality, but it is exactly how a computer works.
Two states, two digits
A computer is built from billions of tiny switches. Each switch is either on or off. There is no "sort of on". So a computer stores everything using just two digits: 1 for on and 0 for off. That is binary.
We count in tens (denary), probably because we have ten fingers. Bit has no fingers and counts in twos.
Place values
In denary, each column is worth ten times the one to its right: units, tens, hundreds. In binary, each column is worth twice the one to its right. Eight columns look like this:
Binary to denary: add up the columns that have a 1 in them. Here that is 64 + 8 + 4 + 1 = 77.
Denary to binary: work from the left and ask, "does this column fit?" Take 77. Does 128 fit? No: write 0. Does 64 fit? Yes: write 1, and you have 13 left. 32? No. 16? No. 8? Yes, leaving 5. 4? Yes, leaving 1. 2? No. 1? Yes. Answer: 01001101.
How big can it get?
With all eight columns set to 1 you get 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. So 8 bits can store any whole number from 0 to 255. That is 256 different values, because 0 counts too.
In the exam
You are asked to convert a denary number to 8-bit binary nearly every year, for 1 mark. Write all 8 digits, including the zeros at the front. 1001101 is not an 8-bit answer; 01001101 is.