Binary, Data and Logic

Computers store everything as bits. Binary numbers, data sizes, ASCII codes and the logic of AND, OR and NOT are the base of all computing.

Key ideas

A bit is a 0 or a 1; 8 bits make a byte; 1 KB is 1,024 bytes and 1 MB is 1,024 KB.
In binary each place is double the one to its right; turn decimal into binary by dividing by 2 and reading the remainders upwards.
An image needs width × height × bits per pixel, divided by 8 to get bytes.
In ASCII each character has a number: A = 65, B = 66, up to Z = 90; one character takes 1 byte.
With b bits there are 2ᵇ different codes.
A truth table lists every row of inputs: 2 inputs give 4 rows, 3 inputs give 8.

Binary	45 = 32 + 8 + 4 + 1 = 101101₂
Sizes	1 byte = 8 bits; 1 KB = 1,024 bytes; 1 MB = 1,024 KB
Image size	100 × 80 pixels × 8 bits ÷ 8 = 8,000 bytes
AND; OR; NOT	True only if both; True if at least one; flips the value
Order of work	brackets and NOT first, then AND, then OR
Fewest bits for m items	the smallest b with 2ᵇ ≥ m: 200 items → 8 bits

A = True, B = True, C = False. Is (A AND B) OR (NOT C) True or False?

Working: work out the brackets and NOT first, then AND, then OR

Answer: True