Understanding Number Systems and Binary

Binary is the language computers speak, using only two digits: 0 and 1. Think of it like a series of light switches - 0 means "off" and 1 means "on". This base 2 system is perfect for computers because their circuits can easily represent these two states.

Denary (or decimal) is what you use every day - it's base 10 with digits 0-9. When you write 238, you're using the denary system without even thinking about it. The largest denary number you can store in 8 bits is 255, which is quite important to remember.

Hexadecimal is base 16, using 0-9 and letters A-F $where A=10, B=11, C=12, D=13, E=14, F=15$. Programmers love hex because it's a neat way to represent binary numbers.

Here's the clever bit: each position in binary represents a power of 2. In an 8-bit system, you get positions worth 128, 64, 32, 16, 8, 4, 2, and 1. For example, 11101110 in binary equals 238 in denary, whilst 16 in denary is simply 00010000 in binary.

Quick tip: A nibble is 4 bits - exactly half a byte! It's called a nibble because it's a "bite" of a byte.